Academic literature on the topic 'Noiseless amplification'

Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still be possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calculate the precision limits on estimating the phase of coherent states using a noiseless linear amplifier by computing its quantum Fisher information and we show that on average, the noiseless linear amplifier does not improve the phase estimate. We also discuss the case where abstention from measurement can reduce the cost for estimation.

According to the fundamental laws of quantum optics, vacuum noise is inevitably added to the signal when one tries to amplify a signal. However, it has been recently shown that noiseless signal amplification can be realized when a phase-sensitive process is involved. Two phase-sensitive schemes, a correlation injection scheme and a two-beam phase-sensitive amplifier scheme, are both proposed to realize multi-way noiseless signal amplification in a symmetrical cascaded four-wave mixing process. We theoretically study the possibility of the realization of four-way noiseless signal amplification by using these two schemes. The results show that the correlation injection scheme can only realize one-way noiseless signal amplification, but that the two-beam phase-sensitive amplifier scheme can lead to four-way noise figure values below 1. Our results here may find potential applications in quantum information processing, e.g., the realization of quantum information tap and quantum non-demolition measurement, etc.

We address de-Gaussification of continuous variables Gaussian states by optimal non-deterministic noiseless linear amplifier (NLA) and analyze in details the properties of the amplified states. In particular, we investigate the entanglement content and the non-Gaussian character for the class of non-Gaussian entangled state obtained by using NL-amplification of two-mode squeezed vacua (twin-beam, TWB). We show that entanglement always increases, whereas improved EPR correlations are observed only when the input TWB has low energy. We then examine a Braunstein-Kimble-like protocol for the teleportation of coherent states, and compare the performances of TWB-based teleprotation with those obtained using NL-amplified resources. We show that teleportation fidelity and security may be improved for a large range of NLA parameters (gain and threshold).

In this thesis, we report the observations of optical squeezing from second harmonic generation (SHG), optical parametric oscillation (OPO) and optical parametric amplification (OPA). Demonstrations and proposals of applications involving the squeezed light and electro-optic control loops are presented. ¶ In our SHG setup, we report the observation of 2.1 dB of intensity squeezing on the second harmonic (SH) output. Investigations into the system show that the squeezing performance of a SHG system is critically affected by the pump noise and a modular theory of noise propagation is developed to describe and quantify this effect. Our experimental data has also shown that in a low-loss SHG system, intra-cavity nondegenerate OPO modes can simultaneously occur. This competition of nonlinear processes leads to the optical clamping of the SH output power and in general can degrade the SH squeezing. We model this competition and show that it imposes a limit to the observable SH squeezing. Proposals for minimizing the effect of competition are presented. ¶ In our OPO setup, we report the observation of 7.1 dB of vacuum squeezing and more than 4 dB of intensity squeezing when the OPO is operating as a parametric amplifier. We present the design criteria and discuss the limits to the observable squeezing from the OPO.We attribute the large amount of squeezing obtained in our experiment to the high escape efficiency of the OPO. The effect of phase jitter on the squeezing of the vacuum state is modeled. ¶ The quantum noise performance of an electro-optic feedforward control loop is investigated. With classical coherent inputs, we demonstrate that vacuum fluctuations introduced at the beam splitter of the control loop can be completely cancelled by an optimum amount of positive feedforward. The cancellation of vacuum fluctuations leads to the possibility of noiseless signal amplification with the feedforward loop. Comparison shows that the feedforward amplifier is superior or at least comparable in performance with other noiseless amplification schemes. When combined with an injection-locked non-planar ring Nd:YAG laser, we demonstrate that signal and power amplifications can both be noiseless and independently variable. ¶ Using squeezed inputs to the feedforward control loop, we demonstrate that information carrying squeezed states can be made robust to large downstream transmission losses via a noiseless signal amplification. We show that the combination of a squeezed vacuum meter input and a feedforward loop is a quantum nondemolition (QND) device, with the feedforward loop providing an additional improvement on the transfer of signal. In general, the use of a squeezed vacuum meter input and an electro-optic feedforward loop can provide pre- and post- enhancements to many existing QND schemes. ¶ Finally, we proposed that the quantum teleportation of a continuous-wave optical state can be achieved using a pair of phase and amplitude electro-optic feedforward loops with two orthogonal quadrature squeezed inputs. The signal transfer and quantum correlation of the teleported optical state are analysed. We show that a two dimensional diagram, similar to the QND figures of merits, can be used to quantify the performance of a teleporter.

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
info:eu-repo/semantics/nonPublished

In the past decade, quantum communication protocols based on continuous variables (CV) has seen considerable development in both theoretical and experimental aspects. Nonetheless, challenges remain in both the practical security and the operating range for CV systems, before such systems may be used extensively. In this thesis, we present the optimisation of experimental parameters for secure randomness generation and propose a non-deterministic approach to enhance amplification of CV quantum state. The first part of this thesis examines the security of quantum devices: in particular, we investigate quantum random number generators (QRNG) and quantum key distribution (QKD) schemes. In a realistic scenario, the output of a quantum random number generator is inevitably tainted by classical technical noise, which potentially compromises the security of such a device. To safeguard against this, we propose and experimentally demonstrate an approach that produces side-information independent randomness. We present a method for maximising such randomness contained in a number sequence generated from a given quantum-to-classical-noise ratio. The detected photocurrent in our experiment is shown to have a real-time random-number generation rate of 14 (Mbit/s)/MHz. Next, we study the one-sided device-independent (1sDI) quantum key distribution scheme in the context of continuous variables. By exploiting recently proven entropic uncertainty relations, one may bound the information leaked to an eavesdropper. We use such a bound to further derive the secret key rate, that depends only upon the conditional Shannon entropies accessible to Alice and Bob, the two honest communicating parties. We identify and experimentally demonstrate such a protocol, using only coherent states as the resource. We measure the correlations necessary for 1sDI key distribution up to an applied loss equivalent to 3.5 km of fibre transmission. The second part of this thesis concerns the improvement in the transmission of a quantum state. We study two approximate implementations of a probabilistic noiseless linear amplifier (NLA): a physical implementation that truncates the working space of the NLA or a measurement-based implementation that realises the truncation by a bounded postselection filter. We do this by conducting a full analysis on the measurement-based NLA (MB-NLA), making explicit the relationship between its various operating parameters, such as amplification gain and the cut-off of operating domain. We compare it with its physical counterpart in terms of the Husimi Q-distribution and their probability of success. We took our investigations further by combining a probabilistic NLA with an ideal deterministic linear amplifier (DLA). In particular, we show that when NLA gain is strictly lesser than the DLA gain, this combination can be realised by integrating an MB-NLA in an optical DLA setup. This results in a hybrid device which we refer to as the heralded hybrid quantum amplifier. A quantum cloning machine based on this hybrid amplifier is constructed through an amplify-then-split method. We perform probabilistic cloning of arbitrary coherent states, and demonstrate the production of up to five clones, with the fidelity of each clone clearly exceeding the corresponding no-cloning limit.

In this thesis, we report the observations of optical squeezing from second harmonic generation (SHG), optical parametric oscillation (OPO) and optical parametric amplification (OPA). Demonstrations and proposals of applications involving the squeezed light and electro-optic control loops are presented. ¶ ...