Tesis sobre el tema "Entanglement of Gaussian states"

2011 - 2012
The Dissertation Quantumness of Gaussian and non-Gaussian states in the op- tical domain collects my personal both theoretical and experimental contribu- tions, in the context of the Quantum Information theory in continuous variables (cv). In this context, the research focused on the analysis of the quantum prop- erties of bipartite states of electromagnetic radiation. The Dissertation contains, rst, the study of the main possible quantum cor- relations between two modes of the electromagnetic eld. Particular attention has been devoted to the analysis of the di¤erent forms of non-locality present in quantum mechanics. Second, it shows the analysis of how the presence of quantum properties in bipartite states a¤ects the performance of these states, when they are used as resources in quantum protocols. In particular, the cv teleportation protocol was used as a reference to test the goodness of results. The quantum resources can be divided in two main classes: Gaussian re- sources and non-Gaussian ones. My research activity has been strucured in which way to be able to proceed, in parallel, to the analysis of both classes. Gaussian resoures.To assess the presence of entanglement in a quantum system it is possible to refer to the many criteria proposed in the literature. In the Dissertation it is reported the study of some main criteria generally used for Gaussian bipartite mixed states. This study has allowed us to establish a hierarchy very useful for the evaluation of the entanglement. Then we have dis- cussed and experimentally analyzed the e¤ects of the transmission over a lossy channel on the quantumness of bipartite Gaussian states, focusing our analysis on the states generated by a type-II optical parametric oscillator (OPO). Even- tually it is reported the study of the Bell s inequality in terms of purity and entanglement for a bipartite Gaussian state, desribed by a symmetric covari- ance matrix..It allows to investigate how the "quantumness" owned by a state, established by the violation of Bell s inequality, is related to the purity of the state and to the entanglement. Non-Gaussian resources. The study of non-Gaussian resources is mainly related to a particular class of states: the squeezed Bell states. All the analy- sis carried out to date show that these states are one of the best possible re- sources for e¢ cient BKV quantum teleportation protocol. This is con rmed by two additional theoretical tests presented in the Dissertation. In fact, squeezed Bell states maximize the violation of Bell s inequality with respect to all other (Gaussian and non-Gaussian) states obtained from the same class. So they represent the most non-local resource among all those considered (for example, the squeezed photon number states, the photon subtracted squeezed states, the photon added states, the squeezed vacuum states). Moreover, as demonstrated in the course of the Dissertation, squeezed Bell states are the best resource for teleportation of a coherent state, even after having undergone a process of en- tanglement swapping. The result is compared with that provided by the other main quantum swapped resources of the same class. As a consequence of the positive results obtained from the tests, it was designed a scheme that allows the experimental production of squeezed Bell states. It is then evaluated its experimental feasibility both in ideal and realistic conditions obtaining very encouraging results. Finally, it is dealt the study (it is at a very preliminary stage) of a non-Gaussian state produced by a sub-threshold OPO, when there are uctuations of some parameters of the optical device (amplitude and phase of the pump, etc..) at the aim to nd a new strategy for the generation of non-Gaussian resources. [edited by author]
XI n.s.

The processing of information based on the generation of common quantum optical states (e.g. coherent states) and the measurement of the quadrature components of the light field (e.g. homodyne detection) is often referred to as continuous-variable quantum information processing. It is a very fertile field of investigation, at a crossroads between quantum optics and information theory, with notable successes such as unconditional continuous-variable quantum teleportation or Gaussian quantum key distribution. In quantum optics, the states of the light field are conveniently characterized using a phase-space representation (e.g. Wigner function), and the common optical components effect simple affine transformations in phase space (e.g. rotations). In quantum information theory, one often needs to determine entropic characteristics of quantum states and operations, since the von Neuman entropy is the quantity at the heart of entanglement measures or channel capacities. Computing entropies of quantum optical states requires instead turning to a state-space representation of the light field, which formally is the Fock space of a bosonic mode.

This interplay between phase-space and state-space representations does not represent a particular problem as long as Gaussian states (e.g. coherent, squeezed, or thermal states) and Gaussian operations (e.g. beam splitters or squeezers) are concerned. Indeed, Gaussian states are fully characterized by the first- and second-order moments of mode operators, while Gaussian operations are defined via their actions on these moments. The so-called symplectic formalism can be used to treat all Gaussian transformations on Gaussian states, including mixed states of an arbitrary number of modes, and the entropies of Gaussian states are directly linked to their symplectic eigenvalues.

This thesis is concerned with the Gaussian transformations applied onto arbitrary states of light, in which case the symplectic formalism is unapplicable and this phase-to-state space interplay becomes highly non trivial. A first motivation to consider arbitrary (non-Gaussian) states of light results from various Gaussian no-go theorems in continuous-variable quantum information theory. For instance, universal quantum computing, quantum entanglement concentration, or quantum error correction are known to be impossible when restricted to the Gaussian realm. A second motivation comes from the fact that several fundamental quantities, such as the entanglement of formation of a Gaussian state or the communication capacity of a Gaussian channel, rely on an optimization over all states, including non-Gaussian states even though the considered state or channel is Gaussian. This thesis is therefore devoted to developing new tools in order to compute state-space properties (e.g. entropies) of transformations defined in phase-space or conversely to computing phase-space properties (e.g. mean-field amplitudes) of transformations defined in state space. Remarkably, even some basic questions such as the entanglement generation of optical squeezers or beam splitters were unsolved, which gave us a nice work-bench to investigate this interplay.

In the first part of this thesis (Chapter 3), we considered a recently discovered Gaussian probabilistic transformation called the noiseless optical amplifier. More specifically, this is a process enabling the amplification of a quantum state without introducing noise. As it has long been known, when amplifing a quantum signal, the arising of noise is inevitable due to the unitary evolution that governs quantum mechanics. It was recently realized, however, that one can drop the unitarity of the amplification procedure and trade it for a noiseless, albeit probabilistic (heralded) transformation. The fact that the transformation is probabilistic is mathematically reflected in the fact that it is non trace-preserving. This quantum device has gained much interest during the last years because it can be used to compensate losses in a quantum channel, for entanglement distillation, probabilistic quantum cloning, or quantum error correction. Several experimental demonstrations of this device have already been carried out. Our contribution to this topic has been to derive the action of this device on squeezed states and to prove that it acts quite surprisingly as a universal (phase-insensitive) optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time. This also brought into surface a paradoxical effect, namely that such a device could seemingly lead to instantaneous signaling by circumventing the quantum no-cloning theorem. This paradox was discussed and resolved in our work.

In a second step, the action of the noiseless optical amplifier and it dual operation (i.e. heralded noiseless attenuator) on non-Gaussian states has been examined. We have observed that the mean-field amplitude may decrease in the process of noiseless amplification (or may increase in the process of noiseless attenuation), a very counterintuitive effect that Gaussian states cannot exhibit. This work illustrates the above-mentioned phase-to-state space interplay since these devices are defined as simple filtering operations in state space but inferring their action on phase-space quantities such as the mean-field amplitude is not straightforward. It also illustrates the difficulty of dealing with non-Gaussian states in Gaussian transformations (these noiseless devices are probabilistic but Gaussian). Furthermore, we have exhibited an experimental proposal that could be used to test this counterintuitive feature. The proposed set-up is feasible with current technology and robust against usual inefficiencies that occur in optical experiment.

Noiseless amplification and attenuation represent new important tools, which may offer interesting perspectives in quantum optical communications. Therefore, further understanding of these transformations is both of fundamental interest and important for the development and analysis of protocols exploiting these tools. Our work provides a better understanding of these transformations and reveals that the intuition based on ordinary (deterministic phase-insensitive) amplifiers and losses is not always applicable to the noiseless amplifiers and attenuators.

In the last part of this thesis, we have considered the entropic characterization of some of the most fundamental Gaussian transformations in quantum optics, namely a beam splitter and two-mode squeezer. A beam splitter effects a simple rotation in phase space, while a two-mode squeezer produces a Bogoliubov transformation. Thus, there is a well-known phase-space characterization in terms of symplectic transformations, but the difficulty originates from that one must return to state space in order to access quantum entropies or entanglement. This is again a hard problem, linked to the above-mentioned interplay in the reverse direction this time. As soon as non-Gaussian states are concerned, there is no way of calculating the entropy produced by such Gaussian transformations. We have investigated two novel tools in order to treat non-Gaussian states under Gaussian transformations, namely majorization theory and the replica method.

In Chapter 4, we have started by analyzing the entanglement generated by a beam splitter that is fed with a photon-number state, and have shown that the entanglement monotones can be neatly combined with majorization theory in this context. Majorization theory provides a preorder relation between bipartite pure quantum states, and gives a necessary and sufficient condition for the existence of a deterministic LOCC (local operations and classical communication) transformation from one state to another. We have shown that the state resulting from n photons impinging on a beam splitter majorizes the corresponding state with any larger photon number n’ > n, implying that the entanglement monotonically grows with n, as expected. In contrast, we have proven that such a seemingly simple optical component may have a rather surprising behavior when it comes to majorization theory: it does not necessarily lead to states that obey a majorization relation if one varies the transmittance (moving towards a balanced beam splitter). These results are significant for entanglement manipulation, giving rise in particular to a catalysis effect.

Moving forward, in Chapter 5, we took the step of introducing the replica method in quantum optics, with the goal of achieving an entropic characterization of general Gaussian operations on a bosonic quantum field. The replica method, a tool borrowed from statistical physics, can also be used to calculate the von Neumann entropy and is the last line of defense when the usual definition is not practical, which is often the case in quantum optics since the definition involves calculating the eigenvalues of some (infinite-dimensional) density matrix. With this method, the entropy produced by a two-mode squeezer (or parametric optical amplifier) with non-trivial input states has been studied. As an application, we have determined the entropy generated by amplifying a binary superposition of the vacuum and an arbitrary Fock state, which yields a surprisingly simple, yet unknown analytical expression. Finally, we have turned to the replica method in the context of field theory, and have examined the behavior of a bosonic field with finite temperature when the temperature decreases. To this end, information theoretical tools were used, such as the geometric entropy and the mutual information, and interesting connection between phase transitions and informational quantities were found. More specifically, dividing the field in two spatial regions and calculating the mutual information between these two regions, it turns out that the mutual information is non-differentiable exactly at the critical temperature for the formation of the Bose-Einstein condensate.

The replica method provides a new angle of attack to access quantum entropies in fundamental Gaussian bosonic transformations, that is quadratic interactions between bosonic mode operators such as Bogoliubov transformations. The difficulty of accessing entropies produced when transforming non-Gaussian states is also linked to several currently unproven entropic conjectures on Gaussian optimality in the context of bosonic channels. Notably, determining the capacity of a multiple-access or broadcast Gaussian bosonic channel is pending on being able to access entropies. We anticipate that the replica method may become an invaluable tool in order to reach a complete entropic characterization of Gaussian bosonic transformations, or perhaps even solve some of these pending conjectures on Gaussian bosonic channels.

Doctorat en Sciences de l'ingénieur
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This thesis probes the usefulness of non-classical correlations within imperfect continuous variable decoherent quantum systems. Although a consistent function and practical usefulness of these correlations is largely unknown, it is important to examine their characteristics in more realistic dissipative systems, to gain further insight into any possible advantageous behaviour. A bipartite separable discordant state under the action of controlled loss on one subsystem was considered. Under these conditions the Gaussian quantum discord not only proved to be robust against loss, but actually improves as loss is intensified. Harmful imperfections which reduce the achievable level of discord can be counteracted by this controlled loss. Through a purification an explanation of this effect was sought by considering system-environment correlations, and found that a flow of system-environment correlations increases the quantumness of the state. Entanglement recovery possibilities were discussed and revealed the importance of hidden quantum correlations along bi-partitions across the discordant state and a classically prepared "demodulating" system, acting in such a way as to partially cancel the entanglement preventing noise. Entanglement distribution by separable states was studied by a similar framework, in an attempt to explain the emergence of quantum entanglement by a specific flow of correlations in the globally pure system. Discord appears to play a less fundamental role compared to the qubit version of the protocol. The strengthening of non-classical correlations can be attributed to a flow of classical and quantum correlations. This work proves that discord can be created in unique ways and, in select circumstances, can act to counteract harmful imperfections in the apparatus. Due to this advantageous behaviour discord indeed may ultimately aid in more applicable "real world" applications, which are by definition decoherent.

Orientadores: Kyoko Furuya e Marcos César de Oliveira
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
Made available in DSpace on 2018-08-14T10:42:52Z (GMT). No. of bitstreams: 1 Missori_RicardoJose_D.pdf: 12608973 bytes, checksum: 25d2abc254d2688f7a4225e0cd2bc6aa (MD5) Previous issue date: 2009
Resumo: Nesta tese, apresentamos dois resultados para a geração de emaranhamento, ambos envolvendo a interação entre átomos e radiação. Na primeira parte, propomos um esquema para geração de estados emaranhados envolvendo os estados eletrônicos de dois íons separados espacialmente, cada qual aprisionado em uma cavidade. Um átomo propagante, que cruza essas cavidades, é responsável pela geração de estados emaranhados do tipo Bell entre os dois íons. Mostramos que para tempos específicos de interação, a geração dos estados emaranhados é não-probabilística. Propostas de átomo e íons, candidatos a implementação do esquema experimental, também são apresentadas. Já segunda parte deste trabalho, investigamos um modelo para a interação de dois campos quânticos ortogonalmente polarizados com uma nuvem de átomos de quatro níveis do tipo-X. Consideramos, para nosso esquema, situações físicas onde os átomos funcionam efetivamente como sendo de dois níveis. Assim, dentro de uma aproximação linearizada do campo, nosso Hamiltoniano efetivo bilinear, que representa a interação átomos-campo, passa a depender da diferença de população entre os dois níveis do ensemble de átomos. Após uma medida condicionada nos átomos, mostramos que os dois modos do campo ficam em estados emaranhados não-Gaussianos, diferentemente do que foi considerado em alguns trabalhos recentes na literatura que abordamos. Como a compressão abaixo do limite de ruído na polarização linear pode ser usada como indicadora de emaranhamento na polarização circular, nós podemos usar a variância das quadraturas, combinada com o critério de inseparabilidade para variáveis contínuas, para complementar o nosso estudo sobre o esquema experimental.
Abstract: In this thesis, we present two results of entanglement generation, both involving atom-radiation interaction. In the first part, we consider a scheme for generation of entangled states involving electronic states of two distant ions, each one placed in a cavity. A flying atom, that crosses these cavities, is responsible for the generation of entangled states of the Bell-type between the two ions. We show that for specific times of interaction, the entangled states are generated and in a non-probabilistic way. We also present a realistic proposal of candidates for atoms and ions for an experimental implementation of this scheme. In the second part of this work, we investigate a model for the interaction of two orthogonally polarized quantum fields with a cloud of X-like four-level atoms. We consider, in our scheme, a physical situation where the atoms act effectively like two-level atoms. Thus, in a linearized approximation for the field, we derive a bilinear effective Hamiltonian representing the atom-field interaction, which depends on the difference of population between the ensemble of two-level atoms. After a conditional measurement in the atomic system, we show that the two field modes ends up in a non-Gaussian entangled states, differently from what has been considered in some recent works in the literature. Since the squeezing below the noise limit in the linear polarization can be used as an indicator of entanglement in the circular polarization, we can use the variances in the quadratures, combined with the inseparability criterion for continuum variables, to complement our study of the experimental scheme.
Doutorado
Física
Doutor em Ciências

Que se passe-t-il quand un système quantique à N corps est brutalement amené loin de son état d’équilibre ? Vers quelle sorte d’état relaxe-t-il et quelle information peut-on extraire de sa dynamique ? Fournir des réponses à ses questions est un problème difficile qui a suscité l’intérêt de toute une communauté de physiciens. Cependant, le coût numérique important requis pour étudier le comportement de ces systèmes, en particulier pour de grandes tailles, a motivé le développement de méthodes numériques et théoriques de pointes. Cette thèse s’inscrit dans la continuité de ces efforts en proposant un ensemble de méthodes basées sur une représentation en termes d’une théorie de champs Gaussiens afin d’étudier l’évolution des systèmes de spins. Plus particulièrement,ces méthodes sont appliquées `a plusieurs modèles inspirés par les expériences d’atomes froids simulant le comportement de systèmes de spins avec un accent particulier sur l’étude des phénomènes de localisations. Cette thèse présente donc des résultats mettant en évidence l’émergence de la localisation dans des systèmes sans désordre par un effet d’interférence appelé cage d’Aharonov-Bohm ; ainsi qu’une dynamique explorant un riche spectre allant de la diffusion balistique`a la localisation, en passant par la diffusion anormale, cela dans un modèle d’Ising quantique avec désordre géométrique — ce dernier exemple présence un scénario bien plus riche que celui offert par la dynamique des particules libres dans un milieu désordonné. Enfin, nous avons exploré la possibilité pour les approches gaussiennes de décrire la dynamique de systèmes interagissant et leur relaxation vers des états thermiques
What happens when a quantum many-body system is brutally driven away fromequilibrium ? Toward which kind of states does it relax and what informationcan one extract from the resulting dynamics ? Providing answers to these questionsis a challenging problem that spured the interest of a whole community ofphysicists. However, the numerical cost required to investigate the behaviour ofthese systems, particularly for large system sizes, motivated the development ofcutting-edge numerical and theoretical techniques.This thesis aims at contributing to these efforts by proposing a set of methodsbased on a representation of the systems in terms of a Gaussian field theory, withthe purpose of studying the evolution of spin systems. More specifically, thesemethods are applied to several models inspired by cold-atoms experiments simulatingthe behaviour of spin systems, with a stress on the study of localizationphenomena. Therefore, this thesis highlights the emergence of localization in systemsdevoid of disorder due to an interference effect, the so-called Aharonov-Bohmcaging; as well as a geometrically disordered quantum Ising model displaying adynamics exploring a rich spectrum ranging from balistic diffusion to anomalousdiffusion, an then localization - this last example offers a scenario richer than theone exhibited by the dynamics of free particles in a disordered medium. Finally,we explored the possibility for Gaussian approaches to describe the dynamics ofinteracting systems and their relaxation toward thermal states

L'objectif de ce travail de recherche est l'étude des posibilités offertes par une nouvelle approche de l'information quantique basée sur des variables quantiques continues. Lorsque ces variables continues sont portées par le champs éléctromagnétique, un grand nombre de protocoles d'information quantique peuvent être implémentés à l'aide de lasers et d'éléments d'optique linéaire standards. Cette simplicité expérimentale rend cette approche très intéressantes d'un point de vue pratique, en particulier pour le développement des futurs réseaux de communications quantiques.

Le travail peut se diviser en deux parties complémentaires. Dans la première partie, plus fondamentale, la relation complexe qui existe entre l'intrication et la nonlocalité de la mécanique quantique est étudiée sur base des variables optiques continues. Ces deux ressources étant essentielles pour l'information quantique, il est nécessaire de bien les comprendre et de bien les caractériser. Dans la seconde partie, orientée vers des applications concrètes, le problème de la correction d'erreur à variables continues est étudié. Pouvoir transmettre et manipuler l'information sans erreurs est nécessaire au bon développemnent de l'information quantique, mais, en pratique, les erreurs sont inévitables. Les codes correcteurs d'erreurs permettent de détecter et corriger ces erreures de manière efficace.

Doctorat en Sciences de l'ingénieur
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Ce mémoire de thèse traite de la non-séparabilité de paires de quasi-particules excitées par résonance paramétrique. Le dispositif expérimental utilisé pendant cette thèse permet de produire un condensat de Bose-Einstein d'hélium métastable. L'utilisation d'un gaz d'atomes ultra-froid permet d'atteindre des températures suffisamment basses afin de pouvoir observer des phénomènes intrinsèquement quantiques : la non-séparabilité de l'état. Dans ce travail, nous utilisons le condensat comme un réservoir cohérent permettant de peupler deux modes d'impulsions. L'avantage de l'hélium métastable est sa grande énergie interne, qui permet la détection électronique de particules uniques. Nous mesurons donc la position et le temps d'impact des particules après un temps de vol de 308 ms, ce qui permet de reconstruire la distribution en impulsion dans le piège. Dans la première contribution théorique de ce travail, nous démontrons que la mesure des fonctions de corrélation à deux et quatre corps permet de quantifier la non-séparabilité d'un état gaussien. Nous dérivons également un critère permettant d'attester la séparabilité de l'état via la seule mesure la fonction de corrélation à deux corps. Dans la partie expérimentale, nous améliorons la machine permettant de produire notre gaz ultra-froid, ainsi que sa stabilité. Par ailleurs, nous mettons en œuvre des techniques originales afin de dévier une partie des atomes et éviter la saturation de notre détecteur. Ces améliorations nous permettent ainsi d'observer la non-séparabilité de l'état
This thesis focuses on the non-separability of pairs of quasi-particles excited by parametric resonance. The experimental setup used here allows the production of a Bose-Einstein condensate of metastable helium. The use of an ultra-cold atomic gas makes it possible to reach sufficiently low temperatures to observe intrinsically quantum phenomena: the non-separability of the state. In this work, we use the condensate as a coherent reservoir to populate two momentum modes. The advantage of metastable helium is its high internal energy, which allows the electronic detection of single particles. We therefore measure the position and the time of impact of the particles after a time of flight of 308 ms, which allows us to reconstruct the in-trap momentum distribution. In the first theoretical contribution of this work, we demonstrate that measuring the two- and four-body correlation functions not only attests to, but also quantifies the non-separability of a Gaussian state. We also derive a new entanglement witness using only the two-body correlation function. In the experimental part, we improve the machine used to produce our ultra-cold gas and enhance its stability. We implement original techniques to deflect part of the atoms and avoid the saturation of our detector. These improvements allow us to observe the non-separability of the state

2011 - 2012
This dissertation was carried out within the framework of the Quantum Information (QI). In particular, I have analyzed the main aspects: the protocol, the quantum states, the conditional measurements, and the decoherence. The protocol. I have studied the teleportation protocol, the entanglement swapping protocol, and the Bell’s inequality (which is the basis of some protocols such as the quantum cryptography). I have dealt with the maximization of the efficiency of each protocol, by acting on the generation of the appropriate quantum states. Starting from the known Squeezed Bell (SB) states that maximize the fidelity of teleportation, I have shown that even for the entanglement swapping protocol and for the violation of the Bell’s inequality, the SB states exhibit better performance than all the other continuous variable (CV) quantum states (for example squeezed vacuum states, subtracted photon squeezed states, added photon squeezed states, squeezed number states). Preparation of quantum states. I have presented an experimental scheme capable of generating, with good approximation, the SB states. I have identified a scheme that is based on conditional measures performed on ancillary quantum states. I have started to study an ideal scheme (free by inefficiencies and decoherence), obtaining the reproduction of the SB states. Then I have introduced the inefficiencies of detection, of the optical elements and of the conditional measurements. In the latter case, the scheme does not exactly reproduce the SB states, but tunable quantum states are obtained, which are very close to SB states. They exhibit a greater teleportation fidelity than all other realistic quantum states that we have analyzed. In addition, in collaboration with Prof. Salvatore Solimeno and Dr. Alberto Porzio of University of Naples "Federico II", I have studied (the work is still at a preliminary stage) the non-Gaussianity introduced by fluctuations in the pump amplitude of the Optical Parametric Oscillator(OPO) below threshold and with non-degenerate polarization. I have proved that such fluctuations lead to an increase of fidelity of teleportation with respect to the not fluctuating (and gaussian) case. Conditional Measurements. In the context of the QI, conditional measurements are used to prepare quantum states and to optimize the transfer of information, as required by the specific protocol. I propose a rather general formulation of the method of conditioning through ancillary measurements, in terms of the characteristic functions. I have considered the case of simultaneous measurements of single-photon, of homodyne detection, and of on/off type (via ideal and realistic POVM). Decoherence. The quantum properties are very sensitive to the interaction of the quantum systems with the external environment. For this reason, a part of this dissertation is devoted to analysis of the evolution of some quantum quantities under the action of the decoherence. In particular, I have studied how the effects of decoherence act on the following quantities: the purity, the quantum correlations, the content of information, the fidelity of teleportation of a coherent state, and the Bell’s inequality of a bi-partite Gaussian state that is transmitted through a realistic channel. I have added the experimental verification to the theoretical study, in collaboration with the University of Naples "Federico II" and under the guidance of Dr. Alberto Porzio and of Prof. Salvatore Solimeno. [edited by author]
XI n.s.

Negli ultimi anni l’entropia di entaglement è stata ampiamente studiata nel campo dell‘integrabilità. Con l‘introduzione del modello a replica è stato possibile portare alla luce le proprietà universali dell’ entropia di entanglement di un sistema bipartito nello stato di vuoto. In questa tesi si è investigato il problema dell’entropia di entanglement di un sistema bipartito in uno stato eccitato di singola particella. In particolare, si è considerata una teoria bosonica libera in un volume finito, in modo da sfruttare al meglio le tecniche dell‘integrabilità. Nel corso di questa analisi, è stato possibile rielaborare il modello a replica in un volume finito grazie ad un raddoppiamento della teoria bosonica che ha indotto una simmetria U(1) su ogni copia del modello. Tale tecnica, nota in letter- atura come doubling trick ha permesso di ricondurre il calcolo dell’entropia di Renyi a un’opportuna espansione in form factors dei campi U(1) implementanti tale simmetria e valutarne il contributo dominante nel limite in cui il volume è grande. I risultati ottenuti per la Second Rènyi entropy mostrano che in tale limite, l’eccesso di entanglement dovuto allo stato eccitato rispetto a quello di vuoto è indipendente dall’energia dello stato stesso e può essere interpretato come quantità che misura l’incertezza sulla localizzazione dell’eccitazione nelle due parti di cui è composto il sistema.

Cette thèse s’intéresse à une approche dite hybride de l’information quantique. Deux approches traditionnellement séparées, variables discrètes et variables continues, sont combinées dans une même expérience nécessitant à la fois comptage de photons (nombre de photons) et détection homodyne (quadratures). Cette architecture hybride a d’abord été utilisée pour générer des états non-gaussiens de la lumière de grande fidélité, par exemple état de Fock et chat de Schrödinger optique,qui correspondent à deux types d’encodages utilisés en information quantique. L’utilisation de détecteurs supraconducteurs à forte efficacité a permis d’obtenir un taux de préparation sans précédent, ce qui facilite l’utilisation ultérieure de ces états. Ces deux types d’état sont ensuite été combinés pour réaliser pour la première fois une intrication hybride entre qubits optiques de nature différente. Son extension à des qutrits a également été obtenue.Ces nouvelles ressources ouvrent la voie à la mise en oeuvre de réseau quantique hétérogène où les opérations et les techniques propres aux variables discrètes et continues peuvent être efficacement combinées.Ce travail de thèse a également été consacré à la mise en oeuvre d’un système de conversion de fréquence à haute efficacité et faible bruit, basé sur deux lasers à fibres synchronisés.Ce convertisseur de fréquence quantique permet non seulement d’étendre les états quantiques à des longueurs d’onde difficilement accessibles avec la technologie actuelle, mais constitue également un détecteur de photons à haute performance, surtout dans le régime infrarouge.Basé sur ce système, plusieurs applications ont ensuite été démontrées, comme la détection infrarouge résolue en nombre de photons et l’imagerie infrarouge ultra-sensible
The thesis focuses on the experimental investigation of the optical hybrid approach forquantum information processing. Specifically, two traditionally separated approaches, i.e.the discrete and the continuous-variable ones, are combined in the same experiment with twodistinct quantum measurements based on photon counting (photon number) and homodynedetection (quadrature components).The optical hybrid approach is first applied to generate high-fidelity non-Gaussian states,e.g. Fock states and Schrödinger cat states, which correspond to two types of qubit encodingsused in optical quantum information. The use of high-efficiency superconducting nanowiresingle-photon detectors leads to an unprecedented preparation rate, which facilitates thesubsequent use of these states. For instance, the two types of states are combined to generatefor the first time a hybrid entanglement between particle-like and wave-like optical qubits, aswell as the extension to hybrid qutrit entanglement. These novel resources may pave the wayto implement heterogeneous networks where discrete and continuous-variable operations andtechniques can be efficiently combined. Additionally, we also experimentally demonstratefor the first time the so-called squeezing-induced micro-macro entangled states.During this PhD, efforts have also been dedicated to implement a high-efficiency andlow-noise frequency up-conversion system based on two synchronized fiber lasers. Suchquantum frequency converter not only permits to extend the spectra of quantum statesto difficultly accessible wavelengths with current technology, but also constitutes a highperformancephoton detector especially in the infrared regime. Based on the conversionsystem, several applications are demonstrated, such as infrared photon-number-resolvingdetection, and few-photon-level infrared imaging

Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis the entanglement of symmetric multipartite states is categorised, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalisation of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterisation of entanglement equivalence classes such as Stochastic Local Operations and Classical Communication (SLOCC) and the Degeneracy Configuration (DC). It is found that SLOCC operations between symmetric states can be described by the Möbius transformations of complex analysis, which allows for a clear visualisation of the SLOCC freedoms and facilitates the understanding of SLOCC invariants and equivalence classes. In particular, explicit forms of representative states for all symmetric SLOCC classes of up to 5 qubits are derived. Well-known entanglement classification schemes such as the 4 qubit entanglement families or polynomial invariants are reviewed in the light of the results gathered here, which leads to sometimes surprising connections. Some interesting links and applications of the Majorana representation to related fields of mathematics and physics are also discussed.

L'objectif de cette thèse concerne la manipulation à l'échelle quantique du champ électromagnétique dans le cadre de l'information quantique à variables continues. Pour ce faire nous mélangeons les outils de l'optique quantique à variables discrètes, où la lumière est décrite en termes de photons, avec l'approche continue, traitant des quadratures du champ. Cette technique permet de produire des états non-classiques décrits par des fonctions de Wigner prenant des valeurs négatives. Nous avons pu générer des états intriqués à partir d'impulsions lumineuses initialement indépendantes et pouvant être séparées par une longue distance, l'intrication s'effectuant au travers d'un canal acceptant de fortes pertes. Nous avons ensuite démontré et caractérisé expérimentalement un protocole non-déterministe permettant d'amplifier de faibles signaux sans en amplifier le bruit quantique, augmentant ainsi le rapport signal sur bruit. Puis nous avons mis en œuvre et comparé expérimentalement différentes mesures de non-gaussianité d'un état quantique : ce caractère propre à une description continue de la lumière est d'un intérêt capital pour l'information quantique. Enfin nous avons développé et testé deux améliorations pour notre dispositif. La première est un amplificateur femtoseconde pour notre laser impulsionnel, qui permettra d'obtenir de meilleurs états de départ pour nos expériences. La deuxième est un appareil capable de discriminer le nombre de photon, donnant ainsi des résultats plus précis que ceux des détecteurs dont nous disposons actuellement qui sont uniquement capable de détecter la présence de photons.

Thesis (PhD)--Stellenbosch University, 2014.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.
AFRIKAANSE OPSOMMING: Hoë-dimensionele kwantumverstrengeldheid bied ’n toename in inligtingskapasiteit per foton. Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum kommunikasie, berekening en teleportasie. Omdat die orbitale hoekmomentum (OAM) modusse van lig ’n oneindig dimensionele Hilbertruimte beslaan, het dit voorlopers geword in die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die potensiaal van OAM verstrengeling van fotone deur die parameters in beide die generering en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat betrokke is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons verifieer kwantumtoetse, soos die Einstein, Podolsky en Rosen (EPR) paradoks vir OAM en die hoekkorrelasies, sowel as ’n skending van ’n Bell-tipe ongelykheid. Deur middel van ’n volledige toestand tomografie, karakteriseer ons die kwantum toestand en wys ons dat dit ’n suiwer, hoogs verstrengel kwantum toestand is. Ons toon ook dat hierdie metode uitgebrei kan word na hoër dimensies. Die eksperimentele tegnieke wat tydens die generasie en meet van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM modusse. Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane parametriese af-omskakeling en demonstreer die uitwerking daarvan op beide OAM en die hoekkorrelasies. Ons het ook veranderinge aan die meting skema gemaak deur die foton pare op die Bessel-Gauss (BG) basis te projekteer. Ons wys dat hierdie metode die gemeetde spiraal bandwydte kan optimeer deur eenvoudig die kontinue radiale parameter van die BG modes te verander. Ons demonstreer dat BG modusse verstrengel kan word in hoër dimensies as die heliese modusse, wat algemeen gebruik word, deur berekeninge te maak en te vergelyk met lineêre entropie en vir beide modusse. Ons wys ook dat kwantumverstrengling akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie, wat die studie van projeksie metings toelaat en voorspel die krag van die saamval korrelasies in ’n verstrengeling eksperiment. Ten slotte, gebruik ons elk van die tegnieke om die effek van ’n storing op OAM verstrengling wat in die BG basis gemeet is, te demonstreer. Ons ondersoek die self-genesingseienskap van BG bundels en wys dat die klassieke eienskap vertaal na die kwantum-gebied. Deur die berekening van die konkurrensie (concurrence), sien ons dat die gemeetde verstrengeling herstel word nadat ’n obstruksie ondervind is.

This thesis studies the manipulation of entanglement in three-qubit quantum systems. I consider the operational setting in which the qubits are distributed to three spatially separated parties. The parties act locally on their quantum systems and share classical communication with one another, a scenario commonly called local operations and classical communication (LOCC). In the LOCC setting, there are two different classes of entanglement in multipartite systems, called the GHZ and W classes, which are inequivalent in the sense that states from one class cannot be transformed into the other without the consumption of additional entanglement. In this thesis, I first show that the LOCC conversion of certain GHZ and W-class states becomes possible by using only one additional ebit (“entangled bit”) of shared entanglement. In many cases, this can be proven as the minimal amount of needed entanglement. I then consider the problem of one-way communication transformations from general three-qubit states into two-qubit maximally entangled states, known as EPR states. An optimal protocol in terms of success probability is provided for W-class states. The success probability of this protocol coincides with the optimal success probability if two of the parties are allowed to act jointly within the same laboratory. In other words, forcing the locality constraint on all three parties does not weaken their capabilities for obtaining bipartite entanglement when starting from a W-class state. I also present that this property holds for certain types of GHZ-class states as well.

Quantum entanglement is a phenomenon which has shown great potential use in modern technical implementations, but there is still much development needed in the field. One major problem is how to measure the amount of entanglement present in a given entangled state. There are numerous different entanglement measures suggested, all satisfying some conditions being of either operational, or more abstract, mathematical nature. However, in contradiction to what one might expect, the measures show discrepancies in the ordering of entangled states. Concretely this means that with respect to one measure, a state can be more entangled than another state, but the ordering may be opposite for the same states using another measure. In this thesis we take a closer look at some of the most commonly occurring entanglement measures, and find examples of states showing inequivalent entanglement ordering for the different measures.
Kvantmekanisk sammanflätning är ett fenomen som visat stor potential för framtida tekniska tillämpningar, men för att kunna använda oss av detta krävs att vi hittar lämpliga modeller att mäta omfattningen av sammanflätningen hos ett givet tillstånd. Detta har visat sig vara en svår uppgift, då de modeller som finns idag är otillräckliga när det gäller att konsekvent avgöra till vilken grad olika tillstånd är sammanflätade. Exempelvis kan en modell visa att ett tillstånd är mer sammanflätat än ett annat, medan en annan modell kan visa på motsatsen - att det första tillståndet är mindre sammanflätat än det andra. En möljig orsak kan ligga i de olika modellernas deifnition, då vissa utgår från operativa definitioner, medan andra grundas på matematiska, abstrakta villkor. I denna uppsats tittar vi lite närmre på några av de mätmodeller som finns, och hittar exempel på tillstånd som uppvisar olika ordning av sammanflätningsgrad beroende på vilken modell som används.

The rise of quantum technology has put control at the centre of advancements in quantum mechanics. The union of quantum mechanics with mathematical control theory is a meeting that is leading to a much deeper insight into our interaction with the bizarre properties of quantum theory. Often, the study of discrete variable systems is the focus for making this union. Here, we look at how control theory may be applied to the continuous variable theory of Gaussian states. Special emphasis is given to control of the covariance matrix of these states, as it is here that we find the entanglement and entropic properties of the state. We begin by exploring some initial results for the geometry of Gaussian states, revealing different manifold structures dependent on symplectic eigenvalue degeneracy. In this geometrical setting a proposal for an extension of Williamson's theorem is put forward and partially completed. It is often interesting to look at restricted sets of Hamiltonians and ask what transformations can be performed with concatenations of their corresponding unitaries. Controllable systems are those for which the entire group of interest is possible to enact. We explore an uncontrollable system in a single mode and give a physical analysis as to why it behaves this way. This leads to ideas to move forwards for a necessary and sufficient condition for control on the symplectic group that has been conjectured since 1972. Later, we transfer to the question of open dynamics. We focus on a particular and ubiquitous channel known as 'lossy' or 'the attenuation channel'. An equation is derived describing the evolution for the symplectic invariants of a Gaussian state undergoing such dynamics. The equation of the former chapter is used to explore the evolution of entropy and entanglement. Optimal protocols are developed for the manipulation of these properties undergoing lossy dynamics.

The Gaussian toolbox of the continuous variables provides for deterministic, high-efficiency operations with non-classical states. Its very Gaussian nature, however, restricts its reach for quantum information and communication applications. This thesis comprises three experimental works, which seek to examine the strengths of this toolbox and address some of its weaknesses. The measurement-based non-linearity of a conditional photon-counting measurement can be used to de-Gaussify' a Gaussian state of light. Here, we propose a continuous variable analog of just such a 'heralding' measurement, replacing a non-deterministic photon-counting measurement with a deterministic measurement of the field quadratures. Such a technique cannot be used to prepare a non-Gaussian state, but it can, on average, yield the same non-Gaussian statistics. We demonstrate this technique by reconstructing the statistics of non-Gaussian photon-subtracted squeezed vacuum states. We then consider the problem of noiseless linear amplification. We experimentally demonstrate that in certain scenarios, the requirement for a physical noiseless linear amplifier can be exchanged for a straightforward post-selection of the measurement record. We apply our 'virtual' noiseless amplifier to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We extract an effective entangled resource stronger than even that achievable with a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of the value of the measurement-based noiseless linear amplifier for quantum key distribution, extracting a secret key from an otherwise insecure regime. Lastly, we turn to the recently popularised measure of all quantum correlations: quantum discord. Quantum discord has emerged as a measure of quantum correlations beyond entanglement, with significant ramifications for our understanding of Gaussian states. Here, we introduce a simple protocol that yields an operational interpretation of quantum discord: that discord describes information only accessible via coherent interactions. We first experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interactions is directly linked to the discord of the original state.

Entanglement is a special correlation of the quantum states of two or more particles. It is also a useful resource enabling us to complete tasks that cannot be done by classical means. As a result, the transformation of entangled states of distant particles by local means arose as an important problem in quantum information theory. In this thesis, we first review some of the studies done on the entanglement transformations. We also develop the necessary and sufficient conditions for the deterministic transformation of W-type states.

Entangled photons are ideally suited to the transmission of photonic quantum information. Mitigating the effects of decoherence is fundamental to distributing photonic entanglement across large distances. One such proposal is entanglement distillation, in which operations on a large ensemble of weakly entangled states generate a smaller ensemble of more strongly entangled states. In this thesis, we experimentally and theoretically analyse various tools required for demonstrating continuous-variable (CV) entanglement distillation, following the proposal by Browne et al., [Phys. Rev. A 67, 062320 (2003)]. Specifically, we propose figures of merit to account for the practical limitations of non-deterministic non-Gaussian operations, and analyse the experimental parameters necessary to optimise them. We develop a source of pulsed two-mode squeezed states, which are the initial states of our entanglement distillation protocol. We use weak-field homodyne detection as a phase-dependent photon counting detector, and demonstrate its utility in conditional state generation. Using these states, we demonstrate sub-binomial light as a tool for benchmarking quantum states. Finally, we applied two-mode weak-field homodyne detection to two entangled states and demonstrate correlations in the photon counting statistics which depend on a joint phase from two independent local oscillators. This setup is sufficient to apply an entanglement witness developed by Puentes et al. [New J. Phys. 12, 033042 (2010)]. Despite encouraging simulations, we do not witness entanglement with this scheme, which we attribute to a noise source unaccounted for in the simulations. Although we do not demonstrate entanglement distillation outright, the tools we develop to do so represent a general, hybrid approach to CV quantum optics. Developing tools such as phase-resolved projective measurement on two-mode states allows us to probe both the wave and particle nature of entangled light at the single-photon level. Using and expanding these techniques to probe larger quantum systems may prove useful in studies of fundamental physics and quantum enhanced technologies.

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CNPq
In this work we analyze the problem of creation of Dicke states through the process of entanglement swapping. First we deal with the tripartite case, presenting a deterministic protocol based on a source of EPR pairs. Still in this topic we show that it is possible to create perfect W states (tripartite Dicke states), even when the EPR source does not yield maximally entangled pairs, with a finite success rate. Subsequently we cope with the n-partite case, for which we present a probabilistic procedure, also employing EPR-pair sources, where the output, whenever successful, is perfect. The analysis of this protocol reveals a critical transition for the success probability, which is characterized in the framework of Landau theory of second order phase-transitions. Finally we proceed with a study of the entanglement between bipartitions of systems described by Dicke states, which allows for the implementation of entanglement witnesses. For each Dicke state we present a highly sensitive witness.
Neste trabalho analisamos o problema de criação de estados de Dicke através de um processo de entanglement swapping. Inicialmente tratamos o caso tripartite, para o qual apresentamos um protocolo determinístico empregando uma fonte de estados EPR. Ainda nesse tópico, mostramos que, com uma taxa de sucesso finita, é possível produzir estados W (estados de Dicke tripartite) perfeitos mesmo quando utilizamos uma fonte de estados EPR não maximamente emaranhados. Em seguida consideramos o caso de n partes, para o qual apresentamos um procedimento probabilístico, também fazendo uso de uma fonte de estados EPR, em que o resultado, sempre que bem-sucedido, é perfeito. A análise deste protocolo revela uma transição crítica, que é caracterizada no contexto da teoria de transição de fase de segunda ordem de Landau. Por ultimo fazemos um estudo do emaranhamento entre bipartições de sistemas descritos por estados de Dicke, que nos permite a implementação de testemunhas de emaranhamento. Para cada estado de Dicke, apresentamos uma testemunha com alta sensibilidade.

This thesis presents an investigation into the generation and characterisation of non-Gaussian states in continuous variable quantum optics. Beginning by placing the study of continuous variables within the context of quantum information processing more generally, we then motivate the need for non-Gaussianity within quantum computing protocols. The focus then narrows to the consideration of two particular sets of non-Gaussian states: orthogonal superposition states and the cubic resource state. The superposition of two orthogonal states has been shown to enhance certain continuous variable quantum information processing protocols that rely on entanglement, and within this section two distinct methods for generating such states are considered. While one of these methods provides a specific example, the other introduces a general orthogonaliser that relies solely on knowledge of the expectation value for the chosen orthogonalising operator in order to produce the superposition. The second case for non-Gaussian state generation employs current results demonstrating the production of a weak approximation of the cubic resource state in order to illustrate the use of such single-mode states to generate multimode states with similar features. These states are implemented as ancillas for a deterministic non-Gaussian gate operation on a system of choice. We show that generating multimode states through this distribution scheme allows an enhancement of the output state to better approximate the nonlinear features. Finally, we consider methods of characterising non-Gaussian states. In particular, we introduce a witness for pure states existing outside of the Gaussian convex hull. Such states exclude Gaussian pure states as well as non-Gaussian states generated from mixtures of squeezed and coherent states, and therefore consist of non-Gaussian states generated from non-Gaussian operations. We present a detection-independent bound for such states based on the generalised quasiprobability distribution.

Photonic entanglement sources are nowadays of central interest in the scientific landscape for their demonstrated applications in quantum information, computation and communication. Required features for a real implementation are obviously high brigthness and purity, but also a precise control of decoherence processes during propagation and the use of many degrees of freedom to enhance the amount of information carried. We developed a new photonic entangled source based on parametric down-conversion within two type-I crystals in a non collinear configuration. A first peculiarity of such source is the very broad angular and spectral distribution exploited. In this way we obtained high brightness even using low pump power. A second peculiarity is the coupling of the source with a Spatial Light Modulator (SLM) allowing the compensation of intrinsic phase term which naturally reduces the state purity till about 0.5. Coupling 10 mrad on both channel, we obtained a purity of about 0.97 with a spectrum of 10 nm, and a purity around 0.90 with more than 60 nm. Starting from such purified source we also realized multi-qubit cluster states exploiting the angular degree of freedom (d.o.f.) of the photons. Here the SLM acts as a C-phase gate entangling polarization and momentum qubits. Furthermore we exploited signal-idler angular correlation to demonstrate the ghost imaging of a pure phase object and we realized a new cryptographic protocol based on non-local phase objects superposition. Our source has also paved the way in simulating system-environment interaction since the SLM allows precise decoherence control. We observed different dynamics of the system entanglement (polarization d.o.f.) modulating the environment spectrum (angular distribution). Then studying the trace distance evolution we demonstrated initial system-environment correlation.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 161-166).
Discriminating between quantum states is an indispensable part of quantum information theory. This thesis investigates state discrimination of continuous quantum variables, focusing on bosonic communication channels and Gaussian states. The specific state discrimination problems studied are (a) quantum illumination and (b) optimal measurements for decoding bosonic channels. Quantum illumination is a technique for detection and imaging which uses entanglement between a probe and an ancilla to enhance sensitivity. I shall show how entanglement can help with the discrimination between two noisy and lossy bosonic channels, one in which a target reflects back a small part of the probe light, and the other in which all probe light is lost. This enhancement is obtained even though the channels are entanglement-breaking. The main result of this study is that, under optimum detection in the asymptotic limit of many detection trials, 6 dB of improvement in the error exponent can be achieved by using an entangled state as compared to a classical state. In the study of optimal measurements for decoding bosonic channels, I shall present an alternative measurement to the pretty-good measurement for attaining the classical capacity of the lossy bosonic channel given product coherent-state inputs. This new measurement has the feature that, at each step of the measurement, only projective measurements are needed. The measurement is a sequential one: the number of steps required is exponential in the code length, and the error rate of this measurement goes to zero in the limit of large code length. Although not physically practical in itself, this new measurement has a simple physical interpretation in terms of collective energy measurements, and may give rise to an implementation of an optimal measurement for lossy bosonic channels. The two problems studied in my thesis are examples of how state discrimination can be useful in solving problems by using quantum mechanical properties such as entanglement and entangling measurements.
by Si Hui Tan.
Ph.D.

Le thème central de cette thèse cumulative est l’étude de l’intrication multi-partite quantique pour des systèmes de dimension finie. Nous avons developpé un algorithme numérique basé sur un problème d’optimisation semi-définie, qui permet de décider si un état est intriqué ou pas en un nombre fini d’itérations. Cet algorithme est une extension d’algorithmes déjà connus qui ne permettent pas de conclure lorsque l’état en question est séparable. Dans notre cas, si l’état est séparable, l’algorithme permet d’obtenir une décomposition de l’état en une mixture d’états séparables. Ces résultats ont été obtenus en exploitant la correspondance entre le problème de l’intrication et le problème des moments tronqués (truncated moment problem). Nous avons aussi développé une nouvelle manière d’exprimer l’état partiellement transposé d’un état symétrique de plusieurs qubits, simplifiant par la-même nombre de résultats bien connus en théorie de l’intrication.Cette nouvelle manière d’écrire le critère de transposée partielle unifie différentes interprétations et formulations alternatives dudit critère, et fait partie intégrante de notre algorithme d’optimisation semi-définie.Nous avons aussi étudié en détails les propriétés géométriques des états intriqués de deux qubits : nous avons pu répondre à la question de savoir à quelle distance un état pur est de l’enveloppe convexe des états symétriques et séparables, en donnant une formule explicite de l’état symétrique et séparable le plus proche — la distance étant celle de Hilbert-Schmidt. Pour les états mixtes nous avons pu obtenir et une borne supérieure numérique et une borne inférieure analytique pour cette distance. Pour un plus grand6nombre de qubits, nous nous sommes intéressés à la boule des états absolument classique,c’est à dire des états symétriques de plusieurs qubits qui restent séparables sous n’importe quelle transformation unitaire. Nous avons trouvé une borne inférieure analytique pour le rayon de cette boule autour de l’état maximallement mixte ainsi qu’une borne supérieure numérique, cette dernière ayant été obtenue en cherchant un état intriqué aussi proche que possible de l’état maximallement mixte.La représentation tensorielle d’un état symétrique de plusieurs qubits, autrement dit de l’état d’un spin j, nous a permis d’étudier des propriétés de l’intrication en nous basant sur le spectre du tenseur (valeurs propres du tenseur). Le caractère défini du tenseur est relié à l’intrication de l’état qu’il représente, donnant la possibilité de détecter la présence d’intrication à l’aide de la valeur propre minimale du tenseur. Toutefois, les valeurs propres du tenseur sont autrement plus compliquée à calculer que les valeurs propres matricielle, rendant l’analyse numérique plus délicate. La relation entre la valeur propre minimale du tenseur et la quantité d’intrication présente dans l’état a aussi été étudiée.Il en ressort que les deux quantités sont étroitement corrélées pour des systèmes de petite taille, c’est à dire jusqu’à six qubits. L’étude de ces corrélations a nécessité une méthode indépendante pour jauger de la quantité d’intrication présente dans un état. Pour cela nous avons amélioré des méthodes numériques pour déterminer la distance entre un état et l’ensemble composé des états symétriques et séparables, en utilisant une combinaison d’algorithmes d’optimisation quadratique et d’optimisation linéaire. La représentation tensorielle des états symétriques de plusieurs qubits a aussi été utilisée pour définir formellement une nouvelle classe de tenseurs, appellés "regularly decomposable tensors",qui correspond à l’ensemble des états symétriques et séparables de plusieurs qubits
The main topic of this compilation thesis is the investigation of multipartite entanglement of finite dimensional systems. We developed a numerical algorithm that detects if a multipartite state is entangled or separable in a finite number of steps of a semi-definite optimization task. This method is an extension of previously known semi-definite methods, which are inconclusive when the state is separable. In our case, if the state is separable, an explicit decomposition into a mixture of separable states can be extracted. This was achieved by mapping the entanglement problem onto the mathematically well studied truncated moment problem.Additionally, a new way of writing the partially transposed state for symmetric multi-qubit states was developed which simplifies many results previously known in entanglement theory. This new way of writing the partial transpose criterion unifies different interpretations and alternative formulations of the partial transpose criterion and it is also a part in the aforementioned semi-definite algorithm.The geometric properties of entangled symmetric states of two qubits were studied in detail: We could answer the question of how far a given pure state is from the convex hull of symmetric separable states, as measured by the Hilbert-Schmidt distance, by giving an explicit formula for the closest separable symmetric state. For mixed states we could provide a numerical upper and analytical lower bound for this distance.For a larger number of qubits we investigated the ball of absolutely classical states, i.e.~symmetric multi-qubit states that stay separable under any unitary transformation. We found an analytical lower bound for the radius of this ball around the maximally mixed symmetric state and gave a numerical upper bound on this radius, by searching for an entangled state as close as possible to the maximally mixed symmetric state.The tensor representation of a symmetric multi-qubit state, or spin-$j$ state, allowed us to study entanglement properties based on the spectrum of the tensor via tensor eigenvalues. The definiteness of this tensor relates to the entanglement of the state it represents and, hence, the smallest tensor eigenvalue can be used to detect entanglement. However, the tensor eigenvalues are more difficult to determine than the familiar matrix eigenvalues which made the investigation computationally more challenging.The relationship between the value of the smallest tensor eigenvalue and the amount of entanglement in the state was also investigated. It turned out that they are strongly correlated for small system sizes, i.e.~for up to six qubits. However, to investigate this correlation we needed an independent way to gauge the amount of entanglement of a state and in order to do so we improved existing numerical methods to determine the distance of a state to the set of separable symmetric states, using a combination of linear and quadratic programming.The tensor representation of symmetric multi-qubit states was also used to formally define a new tensor class of regularly decomposable tensors that corresponds to the set of separable symmetric multi-qubit states

Distributing and sharing entanglement at a distance is a key ingredient in many future quantum communication protocols, however entanglement is a fragile resource and can break down upon interacting with the environment. Within this thesis we present two possible entanglement swapping protocols, and show that these protocols are resilient to small levels of photonic losses. We propose the use of these protocols in quantum communication schemes that require shared entangled qubits, in the form of a Bell state. The input states to our proposed protocols are hybrid entangled states, which are discrete-variable and continuous-variable entangled states. We use the vacuum and single photon Fock state as our discrete half, which is stationary in our entanglement swapping protocol, whereas the continuous variable half is modelled as travelling through lossy optical fibre before being measured. The first protocol uses coherent states in a superposition as propagating modes in our entanglement swapping setup, whereas the second, more complicated, protocol uses superposed cat states. We model photonic losses by applying a beam-splitter of transmission T to our propagating continuous variable modes, along with an input vacuum state. We also model the more realistic circumstance in which the losses in these two continuous variable modes are not equal. We then detect these continuous variable modes using a vacuum projective measurement and balanced homodyne detection. We also investigate homodyne measurement imperfections and non-ideal outcomes, as well as success probabilities of these measurement schemes. We calculate the entanglement negativity and linear entropy of our final two qubit state, as well as fidelity against the |\Phi^+ > Bell state in the coherent state protocol, and a phase-rotated |\Phi^+(\alpha)> Bell state in the cat state regime. We demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol.

In this thesis, the entangled mixed states of two qubits are considered. In the case where the matrix rank of the corresponding density matrix is 2, such a state can be purified to a pure state of 3 qubits. By utilizing this representation, the classification of such states of two qubits by stochastic local operations assisted by classical communication (SLOCC) is obtained. Also for such states, the optimal ensemble that appears in the computation of the concurrence and entanglement of formation is obtained.

In quantum photonics, the requirement for photon pairs with specific quantum states has led to a demand for a fast, high resolution and accurate characterisation of photon pair sources. However, current quantum methods of characterisation suffer from limited accuracy and resolution, and only consist of intensity measurements that prevent access to phase-sensitive measurement photon pairs. A promising tool that addresses these challenges, uses the classical analogue of nonlinear processes to stimulate photon generation, yielding much higher count rates that allows for a higher resolution and accurate photon pair source characterisation. Furthermore, this classical measurement allows for an innovative method to perform full phase-sensitive quantum tomography of photon pair sources that was previous thought to be experimentally challenging to obtain. This thesis examines and compares the quantum and classical method of characterisation of spectral correlations in χ^3 nonlinear devices; namely two integrated silicon nanowires, and a highly nonlinear fibre. In the first study, we use stimulated nonlinear process to confirm the speed-up of characterisation of photon pairs and demonstrate that additional resolution is gained when compared to the traditional coincidence measurements with no increase in measurement time. By applying this technique with phase-sensitive amplification to another identical silicon nanowire, the first phase sensitive measurements are presented showing details that are otherwise hidden in traditional intensity measurements. Furthermore, phase-sensitive measurement of a highly nonlinear fibre shows that phase-sensitive measurements have excellent sensitivity to small features when compared to the traditional intensity measurements.

Bien que la physique des transistors organiques ait été largement étudiée, l'analyse avec la densité d'états Gaussianne fait toujours défaut malgré la nature désordonnée des semi-conducteurs organiques. Étant donné que le transport et l'injection de charges ont lieu à la densité d'états Gaussienne, cette structure énergétique distinctive des semi-conducteurs organiques pourrait rendre le processus d'accumulation de charges, et donc le fonctionnement du dispositif, différent. Cette thèse est consacrée à la compréhension de l'effet de la densité d'états Gaussienne sur les paramètres des transistors organiques, la tension de seuil, la mobilité du porteur de charge et la barrière d'injection via des simulations 2D basées sur des éléments finis numériques et la validation expérimentale. La tension de seuil est comprise par le piégeage de charge dans la secondaire densité d'états Gaussianne ainsi que dans la densité d'états intrinsèque. Nous montrons que le chevauchement des deux densité d'états en raison du désordre induit des comportements de seuil spécifiques des transistors organiques. Deuxièmement, le transport est étudié via le modèle gaussien désordonné sur des sites spatiaux aléatoires de semi-conducteurs organiques. Ce modèle peut offrir un résultat précis par rapport au modèle avec un réseau cubique. De plus, nous proposons une paramétrisation correcte du modèle pour des polymères aux petites molécules. Enfin, la barrière d'injection basée sur la charge et le transport est étudiée et comparée. Les avantages et les limites de chaque modèle sont évalués
Although the device physics of organic field-effect transistors (OFETs) has been widely studied, the analysis with energetic distribution of the density-of-states (DOS) is still lacking in spite of the disordered nature of organic semiconductors. Because charge transport and injection take place at the Gaussian DOS, this distinctive energetic structure of organic semiconductors could make the charge-accumulation process, and hence the device operation, different. This thesis is dedicated to understanding the effect of Gaussian DOS on device parameters of OFETs, the threshold voltage, charge-carrier mobility and injection barrier via numerical finite-element based 2D simulations and experimental validation. The threshold voltage is comprehended by the charge trapping into the secondary Gaussian trap DOS as well as the intrinsic Gaussian DOS. We show that the overlap of two Gaussian DOSs due to the disorder induces specific threshold behaviors of OFETs. Second, the hopping transport is studied via Gaussian disordered model (GDM) on random spatial sites of organic semiconductors. This model can offer a precise result over GDM with cubic lattice. Also, we propose a correct parametrization of the model for wide range of materials from polymers to small molecules. Lastly, charge-based and transport-based injection barrier are studied and compared with Gaussian DOS. The advantages and limits of each model are evaluated

A quantum state represents neither properties of a physical system nor anyone s knowledge of its properties. The important question is not what quantum states represent but how they are used as informational bridges. Knowing about some physical situations (its backing conditions), an agent may assign a quantum state to form expectations about other possible physical situations (its advice conditions). Quantum states are objective: only expectations based on correct state assignments are gen- erally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice con- ditions. This paper o¤ers an account of quantum states and their function

Nanostructures are promising building blocks for quantum technologies due to their reproducible nature and ability to self-assemble into complex structures. However, the need to control these nanostructures represents a key challenge. Hence, this thesis investigates the manipulation and creation of quantum states in certain nanostructures. The results of this thesis can be applied to quantum information processing and to extremely sensitive magnetic-field measurements. In the first research chapter, we propose and examine methods for entangling two (remote) nuclear spins through their mutual coupling to a transient optically excited electron spin. From our calculations we identify the specific molecular properties that permit high entangling power gates for different protocols. In the next research chapter, we investigate another method to create entanglement; this time between two remote electronic spins. This method uses a very sensitive magnetic-field sensor based on a crystal defect that allows the detection of single magnetic moments. The act of sensing the local field constitutes a two-qubit projective measurement. This entangling operation is remarkably robust to imperfections occurring in an experiment. The third research chapter presents an augmented sensor consisting of a nitrogen-vacancy centre for readout and an `amplifier' spin system that directly senses tiny local magnetic fields. Our calculations show that this hybrid structure has the potential to detect magnetic moments with a sensitivity and spatial resolution far beyond that of a sensor based on only a nitrogen-vacancy centre, and indeed this may be the physical limit for sensors of this class. Finally, the last research chapter investigates measurements of magnetic-field strength using an ensemble of spin-active molecules. Here, we describe a quantum strategy that can beat the common standard strategy. We identify the conditions for which this is possible and find that this crucially depends on the decoherence present in the system.

The symplectic formalism applied to the phase-space representation of bosonic quantum systems provides us with a powerful mathematical tool for the characterisation of Gaussian states and transformations. As a consequence, quantum information protocols involving the latter are very well understood from a theoretical point of view. Nevertheless, it has become clear in recent years that the use of non-Gaussian resources is necessary in order to perform various crucial information-processing tasks. An illustration of this fact can for instance be found in situations where a Gaussian no-go theorem precludes the use of Gaussian transformations in order to achieve a task involving Gaussian states, such as quantum entanglement distillation, quantum error correction, or universal quantum computation. In the first part of this thesis, we develop a new method based on the generating function of a sequence, which gives rise to an elegant description of intrinsically non-Gaussian objects. Building on the generating function of the matrix elements of Gaussian unitaries in Fock basis, our approach gives access to the multi-photon transition probabilities via unexpectedly simple recurrence equations. The method is developed for Gaussian unitaries effecting both passive and active linear coupling between two bosonic modes. It predicts an interferometric suppression term which generalises the Hong-Ou-Mandel effect for more than two indistinguishable photons impinging on a balanced beam splitter. Furthermore, it exhibits an unsuspected 2-photon suppression effect in optical parametric amplification of gain 2, which originates from the indistinguishability between the input and output photon pairs. Finally, we extend our method to Bogoliubov transformations acting on an arbitrary number of modes. In the second part of this thesis, we introduce a class of Gaussian-dilatable bosonic quantum channels (characterised by a Gaussian unitary in their Stinespring dilation) called passive-environment channels. These channels are interesting from a quantum thermodynamical viewpoint because they correspond to the coupling of a bosonic system with a bosonic environment that is passive in the Fock-basis (that is, no energy can be extracted from it by using unitary transformations) followed by discarding the environment. Making use of the generating function, we provide a description of these channels in terms of Gaussian bosonic channels. We then introduce a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. We prove various properties of Fock-majorization, showing in particular that the latter can be interpreted as a relation indicating the existence of a heating or amplifying map between two quantum states. This new preorder relation happens to be relevant in the context of passive-environment bosonic channels. Indeed, we show that these channels are Fock-majorization-preserving, so that any two input states that obey a Fock-majorization relation are transformed into output states respecting a similar relation. As a consequence, it also implies that passive-environment channels are majorization-preserving over the set of passive states of the harmonic oscillator. The consequences of majorization preservation are discussed in the context of the so-called entropy photon-number inequality. Most of our results being independent of the specific nature of the system under investigation, they could be generalised to other quantum systems and Hamiltonians, providing new tools that may prove useful in quantum information theory. In the last part of our thesis, we lay out a resource theory of local activity for bosonic systems. We introduce a notion of local-activity distance, and compare it with the work that can be extracted from a quantum state under local unitaries assisted by passive global unitaries. With this framework, we hope to connect the area of continuous-variable bosonic channels together with quantum thermodynamics.
Le formalisme symplectique appliqué à la représentation des systèmes bosoniques dans l'espace des phases donne accès à un outil mathématique puissant pour la caractérisation des états gau-ssiens et transformations gaussiennes. Les protocoles d'information quantique impliquant ces derniers sont d'ailleurs très bien compris d'un point de vue théorique. Toutefois, il s'est avéré clair durant ces dernières années que l'utilisation de ressources non-gaussiennes est nécessaire afin d'effectuer des tâches cruciales de traitement de l'information. En effet, certaines tâches — telles que la distillation d’intrication quantique, le codage quantique ou encore le calcul quantique — impliquant des états gaussiens ne peuvent être effectuées avec des transformations gaussiennes. Dans la première partie de cette thèse, nous développons une nouvelle méthode basée sur la fonction génératrice d'une suite qui donne lieu à une description élégante d'objets intrinsèquement non-gaussiens. Se basant sur la fonction génératrice des éléments de matrice d'unitaires gaussiens dans la base de Fock, notre approche donne accès aux probabilités de transition multi-photon via des équations de récurrence étonnamment simples. La méthode est développée pour des unitaires gaussiens produisant des couplages linéaires passifs et actifs entres deux modes bosoniques. Elle prédit un terme d'interférence destructive qui généralise l'effet Hong-Ou-Mandel pour plus de deux photons indistinguables pénétrant dans un diviseur de faisceau équilibré. De plus, elle met en évidence un effet inattendu de suppression de deux photons dans un amplificateur paramétrique optique de gain 2. Cette suppression résulte de l’indistinguabilité entre les paires de photons d’entrée et de sortie. Finalement, nous étendons notre méthode à des transformations de Bogoliubov agissant sur un nombre de modes arbitraire. Dans la seconde partie de cette thèse, nous introduisons une classe de canaux quantiques bosoniques gaussiens-dilatables (caractérisés par un unitaire gaussien dans leur ``Stinespring dilation") appelés canaux à environnement passif. Ces canaux sont intéressants du point de vue de la thermodynamique quantique puisqu’ils correspondent au couplage d’un système bosonique avec un environnement bosonique qui est passif dans la base de Fock (en d’autres termes, il est impossible d’en extraire de l’énergie avec des transformations unitaires), suivi du rejet de l’environnement. Grâce à la fonction génératrice, nous fournissons une description de ces transformations en termes de canaux quantiques bosoniques gaussiens limités par le bruit du vide. Nous introduisons ensuite une nouvelle relation de pré-ordre appelé ``majorization" de Fock, qui coïncide avec la ``majorization" usuelle pour les états passifs mais induit une autre relation en terme du nombre moyen de bosons, connectant ainsi les concepts d’énergie et de désordre d’un état quantique. Dans ce contexte, nous prouvons des propriétés variées de la ``majorization" de Fock et montrons en particulier que cette dernière peut être interprétée comme une relation indiquant l’existence d’une transformation d’amplification entre deux états quantiques. Cette nouvelle relation de pré-ordre s’avère appropriée dans le contexte des canaux bosonique à environnement passif. En effet, nous montrons que ces canaux conservent la ``majorization" de Fock, de sorte que n’importe quels deux états d’entrée obéissant une relation de ``majorization" de Fock sont transformés en états de sortie vérifiant une relation similaire. En particulier, cela implique que les canaux à environnement passif préservent la ``majorization" pour l'ensemble des états passifs de l’oscillateur harmonique. Les conséquences de la préservation de la ``majorization" sont examinées dans le contexte de la ``entropy photon-number inequality". Étant indépendants de la nature spécifique du système étudié, la plupart de nos résultats peuvent être généralisés à d’autres systèmes et hamiltoniens quantiques, donnant lieu à de nouveaux outils qui pourraient s’avérer utiles en théorie de l’information quantique. Dans la dernière partie de notre thèse, nous mettons en place une théorie de l’activité locale pour les système bosoniques. Nous introduisons une notion de distance en terme d'activité locale et la comparons avec le travail qui peut être extrait d'un état quantique avec des unitaires locaux assistés par des unitaires globaux passifs. Le but à long terme est de se baser sur cette théorie afin de connecter les domaines des canaux bosoniques à variables continues et de la thermodynamique quantique.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished

This work concerns the generation of optical entangled states by means of parametric down-conversion and their applications in the fields of quantum metrology and quantum information. Particularly we studied the manipulation of multiparameter entanglement by means of adaptive optics, demonstrating a way to improve entanglement visibility with type-II downconversion in the case of large detection apertures and a spatial counterpart to quantum dispersion-cancellation. Moreover, we worked on satellite quantum information, demonstrating the feasibility of single photon exchange between a LEO satellite and a ground station.

Quantum entanglement is employed as a resource throughout quantum information science. However, before entanglement can be put to intelligent use, the issues of its production and detection must be considered. This thesis proposes four schemes for producing the bound entangled Smolin state. Three of these schemes produce the Smolin state by means of general quantum gates acting on different initial states - an all-zero state, a GHZ-state and two combined Bell states. The fourth scheme is based on one-qubit operations acting on two-photon states produced by SPDC. Furthermore, a maximum overlap entanglement witness detecting entanglement in the Smolin state is derived. This witness is measurable in three measurement settings with the maximal noise tolerance p=2/3. Lastly, simplified entanglement witnesses for the 4-, 6- and 8-qubit unitary invariant states are derived. These witnesses are measurable in three measurement settings with noise tolerances p=0.1802..., p=0.1502... and p=0.0751..., respectively.

This thesis is devoted to the study of one-dimensional quantum spin chains using matrix product state-based techniques known. We deal mostly with the transverse field Ising model and perturbations. Firstly, we consider an out of equilibrium steady state by applying an energy current. We confirm the phase diagram, the correlations and the entanglement scaling. Subsequently, we introduce two kinds of perturbations. Firstly, we add an interaction that takes the system away from integrability and we study the correlations and the entanglement scaling, determining its phase diagram. Secondly, we weaken the strength of the interaction every nth pair with focus on the simplest case n=2. In every case we compute correlations and central charge (entanglement scaling) and we show that in the presence of an energy current, there is no conservation of energy. Finally, we motivate briefly work on a system that exhibits the Haldane phase.

Cette thèse porte sur la création et la manipulation d'états non gaussiens dans le but de tester les réseaux quantiques hétérogènes émergents. Ces réseaux sont envisagés pour héberger de multiples plateformes physiques, connectées par des lignes de communication optiques. Les états optiques utilisés pour cette communication devront être adaptés à l'encodage de la plateforme physique à laquelle ils sont connectés, ce qui conduit à une variété de stratégies d'encodage possibles. Dans ce travail, nous développons des critères pour tester la qualité des différents encodages et des outils de référence qui garantissent un transfert d'informations fidèle. En outre, nous montrons que plusieurs encodages peuvent être utilisés simultanément dans le même réseau quantique sans perdre leurs propriétés quantiques lors de la conversion. Nous utilisons des oscillateurs paramétriques optiques de haute qualité, produisant des états comprimés monomodes ou bimodes. Grâce à des détecteurs à photons uniques supraconducteurs, nous créons deux encodages optiques différents représentant un système à deux niveaux et un oscillateur harmonique. Le système à deux niveaux correspond à des superpositions d'excitations de nombres de photons, tandis que l'état de l'oscillateur harmonique à des chats de Schrödinger optiques. En créant une intrication entre ces deux encodages différents, il est possible de les utiliser dans des protocoles de réseau. Ces derniers sont intrinsèquement limités par le taux de réussite et la fidélité des mesures de l'état de Bell. Nous présentons une amélioration de la fidélité de l'état de sortie et de la projectivité d'une mesure linéaire tout-optique de l'état de Bell en combinant la détection de photons uniques avec la sélection en quadrature du champ. L'utilisation de l'intrication hybride avec cette mesure hybride de l'état de Bell permet de convertir un qubit d'entrée à deux niveaux en son équivalent en oscillateur harmonique dans une configuration basée sur la téléportation. Après une analyse approfondie des résultats de l'expérience du convertisseur, nous développons un critère pour juger de la non-gaussianité des cohérences quantiques. Ce critère est appliqué à deux systèmes à deux niveaux expérimentaux différents. Enfin, des simulations démontrent qu'une future version de l'expérience pourra comprendre de la génération d'états non gaussiens corrigeables d'erreur. Ce travail encourage l'utilisation de plusieurs encodages dans les réseaux quantiques et fait progresser les méthodes de mesure et de création d'états qui élargissent les capacités des systèmes optiques pour la communication quantique
This thesis focuses on the creation and manipulation of Non-Gaussian states with the goal of testing emerging heterogeneous quantum networks. These networks are envisioned to host multiple physical platforms, that are connected by optical communication lines. The optical states used for this communication will have to be adapted to the encoding of the physical platform they connect to, leading to a variety of possible encoding strategies. In this work, we develop criteria to test the quality of different encodings and benchmark tools that ensure faithful information transfer. Moreover, we show that multiple encodings can simultaneously be used in the same quantum network without losing their quantum properties through conversion. We use high-quality optical parametric oscillators, producing single- or two-mode squeezed states. Together with heralding via superconducting nanowire single-photon detectors, we create two different optical encodings representing a two-level system and a harmonic oscillator. The two-level system corresponds to superpositions of photon-number excitations, while the harmonic oscillator state translates to optical Schrödinger cats. By creating entanglement between those two different encodings, its use in network protocols is possible. Network protocols are intrinsically limited by the success rate and fidelity of Bell-state measurements. We present an improvement in output state fidelity and projectivity of an all-optical linear Bell-state measurement by combining single photon detection with field quadrature selection. Employing hybrid entanglement together with this hybrid Bell-state measurement enables a two-level input qubit to be converted into its harmonic oscillator counterpart in a teleportation-based setup. After thorough analysis of the results of the converter experiment, we develop a criterion to judge the Non-Gaussianity of quantum coherences. This criterion is applied to two different experimental two-level systems. Finally, a stimulative study of the possible generation of error-correctable Non-Gaussian states points the way towards the future of this experiment. This work promotes the use of multiple encodings in quantum networks and advances measurements and state creation methods that expand the capability of optical systems for quantum communication

Nous analysons les caractéristiques d'intrication de quelques matériaux à l'état solide ainsi que des systèmes particuliers d'atomes et de champs en interaction. Une étude détaillée de la riche structure de phase des modèles de spins de basse dimension, décrivant le minéral naturel d'azurite et les composés de coordination à base de cuivre, a révélé des régimes à comportement d'intrication des plus robustes. En utilisant l'approche des systèmes dynamiques, la structure de phase de certains modèles classiques en réseaux hiérarchiques (récursifs) a aussi été étudiée et, pour la première fois, la transition entre régime chaotique et régime périodique au moyen de la bifurcation tangente a été détectée.Nous présentons une description détaillée des propriétés d'intrication de trois atomes piégés dans la limite dispersive. Une relativement simple accordabilité de la force atomique d'interaction de ce système et son étroite relation aux problèmes de frustration magnétique est démontrée. Les effets de propagation de pulses laser intenses dans un système atomique de type [lambda] avec des forces d'oscillateurs différentes sont analysés. Les résultats obtenus sont d'extrême importance dans des problèmes d'information quantique, comme par exemple, dans l'analyse du mécanisme de transfert de population dans des milieux ayant les propriétés définies ci-avant. Enfin, nous avons analysé les effets dissipatifs dans un protocole de distillation de l'intrication à variable continue récemment proposé. Malgré des contraintes additionnelles sur les paramètres du protocole, il est encore possible d'implémenter ce schéma de distillation évoqué ci-avant dans les technologies émergentes
The entanglement features of some solid state materials, as well as of particular systems of interacting atoms and fields are analyzed. A detailed investigation of the rich phase structure of low dimensional spin models, describing the natural mineral azurite and copper based coordination compounds, has revealed regimes with the most robust entanglement behavior. Using the dynamical system approach, the phase structure of some classical models on hierarchical (recursive) lattices has been also studied and, for the first time, the transition between chaotic and periodic regimes by means of tangent bifurcation has been detected.A detailed description of entanglement properties of three atoms trapped in a cavity within the dispersive limit is presented. A relatively simple tunability of the atomic interaction strength of the above system and its close relation to the problems of frustrated magnetism is shown. Furthermore, the propagation effects of two intense laser pulses in a medium of [lambda] atoms with unequal oscillator strengths are investigated. Obtained results are crucial in some problems of quantum information theory, as, e.g., in the analysis of population transfer mechanism in media possessing the above properties. Finally, the dissipation effects in a recently proposed compact continuous-variable entanglement distillation protocol have been analyzed. Despite additional constraints on the parameters of the protocol, the discussed entanglement distillation scheme in quantum memories is still possible to implement within emerging technologies

PolarizaÃÃo quÃntica tem sido usada extensivamente no processo da informaÃÃo quÃntica e emaranhamento quÃntico à essencial para muitas Ãreas de pesquisas, incluindo computaÃÃo quÃntica. Nesse trabalho foi realizada uma investigaÃÃo do grau de polarizaÃÃo e do emaranhamento de uma famÃlia de estados quÃnticos conhecidos como estados coerentes de fÃtons adicionados. Tais estados podem ser Ãteis na distribuiÃÃo quÃntica de chaves e distribuiÃÃo de emaranhamento. Usamos os parÃmetro de Stokes e a funÃÃo Q para demonstrar que, de uma forma geral, a polarizaÃÃo de uma superposiÃÃo de dois estados coerentes bimodais de fÃtons adicionados aumenta significantemente com o nÃmero de fÃtons adicionados. TambÃm utilizamos a concorrÃncia para mostrar que a quantidade de emaranhamento nas superposiÃÃes citadas apresenta um comportamento que depende se o nÃmero de fÃtons adicionados em cada modo sÃo iguais ou diferentes.
Polarization has been used extensively in quantum information processing, and quantum entanglement is essential to many areas of research, including quantum computing. Here we investigate the degree of polarization and the entanglement of a family of quantum states known as photon-added entangled coherent states. Such states could serve as means of entanglement distribution and quantum key distribution. Using the quantum Stokes parameters and the Q function, we demonstrated that, in general, the polarization of a superposition of two two-mode photon-added coherent states increases significantly with the number of added photons. And using the concurrence, we showed that the amount of entanglement in this kind of superposition presents a behavior that is dependent on whether or not the number of added photons on each mode is the same.

In southern Africa, as elsewhere, the tendency of Iron Age (CE 200-1900) researchers has been to focus on the more prominent places on the landscape, especially those believed by pioneering archaeologists to have been centres of big states. Consequently, most research foci were accorded to Mapungubwe, Great Zimbabwe, Khami, Danamombe and many other places considered as centres (mizinda) of expansive territorial states. However, landscapes away from, and in-between these states and their centres are traditionally viewed as ‘peripheries' where resources that made them prosperous were extracted. The inhabitants of such ‘peripheries' are presented as if they possessed little or no agency. One such area is Mberengwa, a gold-rich area situated between the edges of Mapela, Mapungubwe, Great Zimbabwe, Danamombe, and Khami. This thesis explores the archaeology of Chumnungwa, a drystone-walled muzinda located in Mberengwa. Because of abundant gold, and a landscape optimal for cattle production and crop agriculture, Chumnungwa is often marginalised as a docile ‘periphery' of the more powerful and territorial states that surrounded it. Stratigraphic excavations were performed in different parts of the site to recover artefactual and chronological evidence. Indications are that the inhabitants of Chumnungwa exploited locally acquired resources such as gold, iron, and soapstone, but mixed these with resources from distant areas. Cumulatively, this evidence, when assessed in relation to chronology, suggests that Chumnungwa flourished more or less at the same time as Mapela, and the later phases of Mapungubwe, Great Zimbabwe, Khami, and Danamombe. As a powerful actor in Mberengwa, Chumnungwa also networked and was therefore entangled not only with local, but also with regional, and inter-regional politicoeconomic processes. This suggests it is only a historical invention that can marginalise some landscapes as ‘peripheral', especially in the absence of research, but once attention is directed to them, multiple layers of agency and entanglement emerge.