Dissertations / Theses on the topic 'Quantum noise'

We have conducted an experimental study of the quantum shot noise in a mono-layer graphene device. Conductance of the device and the quantum Hall effect were also investigated. A theoretical model, describing conductance and quantum shot noise in ideal (ballistic) graphene was proposed by Tworzydlo et al., 2006. In diffusive graphene, that is much easier achievable experimentally, shot noise was investigated numerically by several authors (San-Jose et al., 2007, Lewenkopf et al., 2008, Logoteta et al., 2013). Conclusions of the first experimental works (DiCarlo et al., 2008 and Danneau et al., 2008), addressing this problem, didn't lead to an enough broad understanding of it and a further investigation was required. In our experiment we intended to maximally reduce the contributions of the measurement system to the detected signal by performing four-point voltage noise measurement as well as by using cross-correlation detection. In addition to that, our measurement system include home-made cryogenic low-noise amplifiers combined with band-pass filters, while our experimental device carries a constriction in the center of graphene layer and side-gates are used instead of back-gate. First, using the results of the conductance and of the quantum Hall effect measurements we determined the mean free path in our sample and concluded that it was in diffusive regime. The extracted values of the Fano factor show a good agreement with the above-mentioned simulations for this regime, in particular, the peak at Dirac point, predicted by Lewenkopf et al., was observed. Moreover our results are consistent with those of Danneau et al. and DiCarlo et al.

The nature of phase noise in quantum optics is analyzed. In an experiment involving the measurement of the electromagnetic field the two quantities of interest are the energy and phase of the field. However, measurements of the quantities produce quantum fluctuations. The quantum fluctuations are regarded as noise in the treatment presented here. The quantum system is represented by a probability distribution, the Wigner function, and the quantum fluctuations are treated as stochastic noise associated with the quantity being measured. The difficulties of associating a quantum operator with the phase of the system are reviewed and the related energy-phase uncertainty relation is discussed. The alternate interpretation of the phase noise of a quantum system as being the classical phase noise of the Wigner function is presented. In particular the energy and phase noise of the vacuum state, the coherent state, the squeezed state and the squeezed vacuum are discussed in this way. The squeezed states of light are minimum uncertainty states with respect to the quadrature operators and exhibit noise of one quadrature below the noise level associated with the vacuum. The reduced noise level in one quadrature of the field underlies the importance of squeezed states in many practical applications where there is a need to reduce the quantum noise of one quadrature of coherent light. The periodic phase operator eliminates the difficulties associated with the multivalued nature of phase. The analysis of the vacuum and intense coherent state of Carruthers and Nieto by employing periodic phase operators is reviewed, particularly with respect to the energy-phase uncertainty relations and we generalize the approach to develop a phase operator analysis of the squeezed state in the intense field and vacuum limits. We demonstrate here for the first time that the phase operator is simply related to the phase of the squeezed state in the intense field limit and that the squeezed state is approximately an energy-phase minimum uncertainty state in the low-squeezing limit. Also we enlarge on previous work to demonstrate that the phase operator corresponds simply and unambiguously to the phase of the squeeze parameter for the strongly squeezed vacuum and the intensely squeezed vacuum is an energy-phase minimum uncertainty state for some values of phase. The occurrence of squeezing for the case of two coupled quantum oscillators is presented. The system consisting of one mode of the electromagnetic field coupled to a spinless nonrelativistic electron subjected to an harmonic potential is represented by two coupled harmonic oscillators. The dynamics are compared for the case that the rotating wave approximation is employed and for the case that the counter-rotating terms are included. These calculations have not been performed before. The parametric amplifier Hamiltonian with a nonresonant coupling is also studied in order to provide insight into the effects of the counter-rotating terms. Squeezing of the field produced by the electron is a consequence of the inclusion of the counter-rotating terms. The case of a spinless nonrelativistic electron subject to an harmonic potential and coupled to a continuum of electromagnetic field modes is also considered. The case of two coupled oscillators discussed above is generalized by replacing the oscillator which represents the single-mode field by a bath of oscillators. The effects of including counter-rotating terms and of ignoring the counter - rotating terms in the Hamiltonian are compared. The interaction is assumed to produce a frequency shift and an exponential damping term for the oscillating electron. The frequency shift is assumed to be small in either case and so the Wigner-Weisskopff approximation is employed to solve the equations of motion. We demonstrate the new results that dissipation-induced phase-dependent noise is a consequence of including the counter-rotating terms and that the noise is phase-independent for the case that the counterrotating terms are excluded. The relation between these results and recent work on quantum tunnelling in superconducting quantum interference devices is discussed. We conclude by suggesting further research related to the work in this thesis.

Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes.

Large quantum computers have the potential to vastly outperform any classical computer. The biggest obstacle to building quantum computers of such size is noise. For example, state of the art superconducting quantum computers have average decoherence (loss of information) times of just microseconds. Thus, the field of quantum error correction is especially crucial to progress in the development of quantum technologies. In this research, we study quantum error correction for general noise, which is given by a linear Hermitian map. In standard quantum error correction, the usual assumption is to constrain the errors to completely positive maps, which is a special case of linear Hermitian maps. We establish constraints and sufficient conditions for the possible error correcting codes that can be used for linear Hermitian maps. Afterwards, we expand these sufficient conditions to cover a large class of general errors. These conditions lead to currently known conditions in the limit that the error map becomes completely positive. The later chapters give general results for quantum evolution maps: a set of weak repeated projective measurements that never break entanglement and the asymmetric depolarizing map composed with a not completely positive map that gives a completely positive composition. Finally, we give examples.

The purpose of this study is to investigate the effects of noise in quantum simulation. An existing and simple model was used to simulate the results of the evolution of an initial quantum state. The results show that if all states align in z-axis, the dynamical map is completely positive, and the spin bath affected how fast the system evolved. If precessing states are considered, the dynamical map is non completely positive. Visualization of the Bloch vector was used to illustrate the process of the evolution of the quantum system.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.
Includes bibliographical references (p. 393-399).
Good quantum mechanical descriptions of noise evolution with propagating optical waves are critical to understanding the processes which currently limit the generation of squeezed radiation in nonlinear materials. In the first part of this dissertation a general quantum optical model is developed from fundamental principles to describe optical propagation in a broad variety of nonlinear media. The central distinction of the resulting Quantum Macroscopic Propagation Model ( QMPM) is that material susceptibilities, representing the field's interaction with matter, are replaced with quantum mechanical operators. These quantum material operators are shown to comprise material response functions corresponding to the semiclassical susceptibilities and material noise operators representing the true quantum mechanical nature of the material. The material noise operators play important roles in the noise evolution of propagating fields. The Quantum MacrQscopic Propagation Model is compared with the Langevin techniques of statistical mechanics and is shown to correspond to a quasi-rigorous generalized quantum Langevin model. The QMPM correctly indicates the form of the noise operators associated with any particular order of nonlinearity. In the second part a specific model for squeezing in fiber is developed from the general QMPM. Dispersion, linear loss, Raman scattering, forward Brillouin scattering (GAWBS), and two-photon absorption are incorporated into the model, which is linearized and solved for the continuous-wave case. The model successfully predicts several interactions between nonlinearity, dispersion, and noise. It is shown that low levels of two-photon absorption resulting from germanium-doping of fiber may impose critical limits on fiber squeezing. Forward Brillouin scattering is shown to behave exactly as low-frequency Raman scattering and to seriously limit fiber squeezing at low frequencies. The cw composite model is applied to the parameters of several fiber squeezing experiments described in the literature, and the model is shown to predict with fair accuracy the squeezing results in most cases, including soliton squeezing when Lai's effective soliton nonlinear phase shift is used as the phase shift parameter for the model. Simplified expressions are obtained relating the optimal squeezing available to the nonlinear parameters of a particular experiment or new material.
by Jeffrey K. Bounds.
Sc.D.

Rapid developments in experiments provide promising platforms for realising quantum computation and quantum simulation. This, in turn, opens new possibilities for developing useful quantum algorithms and explaining complex many-body physics. The advantages of quantum computation have been demonstrated in a small range of subjects, but the potential applications of quantum algorithms for solving complex classical problems are still under investigation. Deeper understanding of complex many-body systems can lead to realising quantum simulation to study systems which are inaccessible by other means. This thesis studies different topics of quantum computation and quantum simulation. The first one is improving a quantum algorithm in adiabatic quantum computing, which can be used to solve classical problems like combinatorial optimisation problems and simulated annealing. We are able to reach a new bound of time cost for the algorithm which has a potential to achieve a speed up over standard adiabatic quantum computing. The second topic is to understand the amplitude noise in optical lattices in the context of adiabatic state preparation and the thermalisation of the energy introduced to the system. We identify regimes where introducing certain type of noise in experiments would improve the final fidelity of adiabatic state preparation, and demonstrate the robustness of the state preparation to imperfect noise implementations. We also discuss the competition between heating and dephasing effects, the energy introduced by non-adiabaticity and heating, and the thermalisation of the system after an application of amplitude noise on the lattice. The third topic is to design quantum algorithms to solve classical problems of fluid dynamics. We develop a quantum algorithm based around phase estimation that can be tailored to specific fluid dynamics problems and demonstrate a quantum speed up over classical Monte Carlo methods. This generates new bridge between quantum physics and fluid dynamics engineering, can be used to estimate the potential impact of quantum computers and provides feedback on requirements for implementing quantum algorithms on quantum devices.

Quantum-enabled technologies promise advancements across a huge range of industrial, metrological and medical applications and are already demonstrating significant impacts, especially in the realm of sensing and metrology. While the extreme sensitivity of quantum systems to their environment is fueling those applications, it also represents a major hurdle to technologies which require long-term stability such as quantum computing and quantum simulations. In addition to the inherent decoherence phenomenon, the challenge associated with controlling a quantum system accurately and precisely, does in fact impede all of the aforementioned applications. Such techniques have therefore been subject to extensive research in both the academic and industrial sector and as a result, sophisticated quantum control techniques are emerging in order to understand, characterize and mitigate errors in quantum systems. This thesis presents how quantum control techniques can be employed to characterize and suppress both control imperfections and environmental noise in quantum systems, using experiments with trapped ions as a model quantum platform. We demonstrate two distinct but interrelated approaches that leverage either time-domain or frequency-domain information about the noise. In the first approach, we show how supervised learning algorithms can efficiently extract time-domain correlations from time-stamped sequences of projective measurements on a qubit. This information can then be used to perform real-time predictive control in which we autonomously pre-compensate anticipated qubit noise in order to stabilize the system. The second approach deploys provably optimal narrowband controls in order to characterize the specific spectral components of noise experienced by a qubit. Here, frequency-shifted Slepian functions permit reconstruction of system noise with maximum out-of-band rejection, and full spectrum reconstruction is enabled using techniques based on multitaper and Bayesian methods.

This thesis is about probing aspects of the foundations of quantum mechanics. Firstly, two notions of quantum nonlocality are explored: EPR-steering, the ability to control a remote quantum state, and Bell nonlocality, the inconsistency of a theory with local causality. A necessary and sufficient witness of Einstein-Podolsky- Rosen (EPR) steering is derived for a two qubit system employing only correlations between two arbitrary dichotomic measurements on each party. It is demonstrated that all states that are EPR-steerable with such correlations are also Bell nonlocal, a surprising equivalence between these two fundamental concepts of quantum mechanics. Next, testing modifications of the quantum mechanical canonical commutation relations is addressed. These are properties of some quantum gravity theories that involve an effective minimal length. It is shown that optomechanical probes of position noise spectrum of macroscopic oscillators can produce constraints on these theories. A comparison with current and future realistic experiments reveals the potential to beat constraints from direct experiments on elementary particles. Finally, it is studied how such modifications of quantum mechanics manifest in the theory of general continuous quantum position measurements. Several behaviours are found that deviate strongly from that of standard commutation relations.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Title as it appears in MIT Commencement Exercises program, June 2013: Sensitivity improvement of a LIGO gravitational Wayne detector through squeezed state injection. Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (p. 217-223).
Direct detection of gravitational waves will require earth based detectors to measure strains of the order 10-21, at frequencies of 100 Hz, a sensitivity that has been accomplished with the initial generation of LIGO interferometric gravitational wave detectors. A new generation of detectors currently under construction is designed improve on the sensitivity of the initial detectors by about a factor of 10. The quantum nature of light will limit the sensitivity of these Advanced LIGO interferometers at most frequencies; new approaches to reducing the quantum noise will be needed to improve the sensitivity further. This quantum noise originates from the vacuum fluctuations that enter the unused port of the interferometer and interfere with the laser light. Vacuum fluctuations have the minimum noise allowed by Heisenberg's uncertainty principle, [Delta]X1 [Delta]X2 >/=1, where the two quadratures X1 and X2 are non-commuting observables responsible for the two forms of quantum noise, shot noise and radiation pressure noise. By replacing the vacuum fluctuations entering the interferometer with squeezed states, which have lower noise in one quadrature than the vacuum state, we have reduced the shot noise of a LIGO interferometer. The sensitivity to gravitational waves measured during this experiment represents the best sensitivity achieved to date at frequencies above 200 Hz, and possibly the first time that squeezing has been measured in an interferometer at frequencies below 700 Hz. The possibility that injection of squeezed states could introduce environmental noise couplings that would degrade the crucial but fragile low frequency sensitivity of a LIGO interferometer has been a major concern in planning to implement squeezing as part of baseline interferometer operations. These results demonstrate that squeezing is compatible with the low frequency sensitivity of a full scale gravitational wave interferometer. We also investigated the limits to the level of squeezing observed, including optical losses and fluctuations of the squeezing angle. The lessons learned should allow for responsible planning to implement squeezing in Advanced LIGO, either as an alternative to high power operation or an early upgrade to improve the sensitivity. This thesis is available at DSpace@MIT and has LIGO document number P1300006.
by Sheila E Dwyer.
Ph.D.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
19
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 57-58).
Flying in the face of the long-sought-after goal of building optical quantum computers, we show that traditional approaches leveraging nonlinear-optical cross phase modulation (XPM) to construct the critical element, the cphase gate - a gate which seeks to impart a [pi]-radian phase shift on a single photon pulse, conditioned on the presence of a second single photon pulse - are doomed to fail. The traditional story told in common textbooks fails to account for the continuous-time nature of the real world. Previous work addressing this fact - finding that that the proper continuous-time theory introduces fidelity-degrading phase noise that precludes such proposals - was limited in scope to the case of co-propagating pulses with equal group velocities. This left room for criticism that a high-fidelity cphase gate might be constructed using XPM with pulses that pass through each other. In our work, we build such a continuous-time quantum theory of XPM for pulses that pass through each other and evaluate its consequences. We find that fundamental aspects of the real world prevent one from constructing a perfect cphase gate, even in theory, and we show that the best we can do seems to fall far short of what is needed for quantum computation, even if we are extremely optimistic.
by Justin Dove.
S.M.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.
Includes bibliographical references (leaves 49-50).
Two low-noise, high quantum efficiency, high bandwidth photodetectors have constructed to form a balanced homodyne detector to detect squeezed light. The detectors have quantum efficiencies of 85% and 90%, a bandwidth of 1MHz, and a dark noise of ... at 1MHz.
by Elizabeth Caryn Bullard.
S.B.

One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment. One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties. These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical. In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity. In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise. A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus. Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form. Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system.
Um dos objetivos principais da teoria de sistemas quânticos abertos é desenvolver métodos que ajudem a preservar as propriedades quânticas de um sistema interagindo com o ambiente. Um possível caminho para alcançar essa meta é usar reservatórios não-Markovianos, caracterizados por refluxos de informação e renascimento de certas propriedades quânticas. Esses reservatóris geralmente requerem o uso de técnicas avançadas de engenharia, o que pode tornar sua implementação impraticável. Nessa dissertação nós propomos uma técnica alternativa: a injeção de um ruído colorido clássico, o qual induz a desejada não-Markovianidade quântica. De modo a fazer isso, nós investigamos a dinâmica de um sistema quântico interagindo com o ambiente e sob a injeção de um ruído colorido clássico estocástico. Uma equação mestra local no tempo é derivada usando-se do formalismo da função de onda estocástica e de técnicas de cálculo funcional. Após isso, a não-Markovianidade da evolução é detectada através da medida de Andersson, Cresser, Hall e Li, a qual é baseada nos coeficientes da equação mestra na forma de Lindblad-like canônica. Finalmente, nós calculamos a medida para três diferentes ruídos coloridos e estudamos a relação entre o ambiente e o bombeio estocástico necessária para induzir não-Markovianidade quântica, assim como o balanço de energia do sistema.

Light is an ideal information carrier for quantum networks: its quantum properties are not degraded by noise in ambient conditions and it has a large information capacity owing to its high bandwidth. However, quantum technologies based on photonic networks have been hampered by the exponentially poor scaling of the underlying probabilistic quantum operations. Quantum optical memories, devices that store, manipulate, and release on- demand quantum light, have been identified as an indispensable network component, because they facilitate scalability. Noise-free operation of the memory is critical, since even small additional noise can render the memory classical by destroying the quantum character of the light. Here I introduce a new broadband quantum memory protocol - the off-resonant cas- caded absorption (ORCA) memory - that is inherently noise-free and operates in ambient conditions. I model ORCA theoretically, after which I characterise the classical perfor- mance of a proof-of-concept implementation in warm caesium vapour, using weak near- infrared coherent states. In order to verify quantum operation of the ORCA memory, I interface it with a broadband heralded single-photon source. I measure and compare the quantum statistics of the stored and retrieved light, observing for the first time their full preservation in a room-temperature atomic quantum memory. Finally, I make headway into integrating the ORCA vapour memory by investigating an alkali-filled hollow-core fibre platform. I use light-induced atomic desorption (LIAD) to demonstrate record- breaking alkali vapour densities in fibre, a prerequisite for efficient memory operation. Because of its technical simplicity and integrability, its high bandwidth and its low noise, ORCA provides a viable route towards next generation, photonic quantum network technologies.

The argument of this thesis might be summed up as the exploitation of the noise to generate better noise. More specifically this work is about the possibility of exploiting classic noise to effectively transmit quantum information and measuring quantum noise to generate better quantum randomness. What do i mean by exploiting classical noise to transmit effectively quantum information? In this case I refer to the task of sending quantum bits through the atmosphere in order set up transmissions of quantum key distribution (QKD) and this will be the subject of Chapter 1 and Chapter 2. In the Quantum Communications framework, QKD represents a topic with challenging problems both theoretical and experimental. In principle QKD offers unconditional security, however practical realizations of it must face all the limitations of the real world. One of the main limitation are the losses introduced by real transmission channels. Losses cause errors and errors make the protocol less secure because an eavesdropper could try to hide his activity behind the losses. When this problem is addressed under a full theoretical point of view, one tries to model the effect of losses by means of unitary transforms which affect the qubits in average according a fixed level of link attenuation. However this approach is somehow limiting because if one has a high level of background noise and the losses are assumed in average constant, it could happen that the protocol might abort or not even start, being the predicted QBER to high. To address this problem and generate key when normally it would not be possible, we have proposed an adaptive real time selection (ARTS) scheme where transmissivity peaks are instantaneously detected. In fact, an additional resource may be introduced to estimate the link transmissivity in its intrinsic time scale with the use of an auxiliary classical laser beam co-propagating with the qubits but conveniently interleaved in time. In this way the link scintillation is monitored in real time and the selection of the time intervals of high channel transmissivity corresponding to a viable QBER for a positive key generation is made available. In Chapter 2 we present a demonstration of this protocol in conditions of losses equivalent to long distance and satellite links, and with a range of scintillation corresponding to moderate to severe weather. A useful criterion for the preselection of the low QBER interval is presented that employs a train of intense pulses propagating in the same path as the qubits, with parameters chosen such that its fluctuation in time reproduces that of the quantum communication. For what concern the content of Chapter 3 we describe a novel principle for true random number generator (TRNG) which is based on the observation that a coherent beam of light crossing a very long path with atmospheric turbulence may generate random and rapidly varying images. To implement our method in a proof of concept demonstrator, we have chosen a very long free space channel used in the last years for experiments in Quantum Communications at the Canary Islands. Here, after a propagation of 143 km at an altitude of the terminals of about 2400 m, the turbulence in the path is converted into a dynamical speckle at the receiver. The source of entropy is then the atmospheric turbulence. Indeed, for such a long path, a solution of the Navier-Stokes equations for the {atmospheric flow in which the beam propagates is out of reach. Several models are based on the Kolmogorov statistical theory, which parametrizes the repartition of kinetic energy as the interaction of decreasing size eddies. However, such models only provide a statistical description for the spot of the beam and its wandering and never an instantaneous prediction for the irradiance distribution. These are mainly ruled by temperature variations and by the wind and cause fluctuations in the air refractive index. For such reason, when a laser beam is sent across the atmosphere, this latter may be considered as a dynamic volumetric scatterer which distorts the beam wavefront. We will evaluate the experimental data to ensure that the images are uniform and independent. Moreover, we will assess that our method for the randomness extraction based on the combinatorial analysis is optimal in the context of Information Theory. In Chapter 5 we will present a new approach for what concerns the generation of random bits from quantum physical processes. Quantum Mechanics has been always regarded as a possible and valuable source of randomness, because of its intrinsic probabilistic Nature. However the typical paradigm is employed to extract random number from a quantum system it commonly assumes that the state of said system is pure. Such assumption, only in theory would lead to full and unpredictable randomness. The main issue however it is that in real implementations, such as in a laboratory or in some commercial device, it is hardly possible to forge a pure quantum state. One has then to deal with quantum state featuring some degree of mixedness. A mixed state however might be somehow correlated with some other system which is hold by an adversary, a quantum eavesdropper. In the extreme case of a full mixed state, practically one it is like if he is extracting random numbers from a classical state. In order to do that we will show how it is important to shift from a classical randomness estimator, such as the min-classical entropy H-min(Z) of a random variable Z to quantum ones such as the min-entropy conditioned on quantum side information E. We have devised an effective protocol based on the entropic uncertainty principle for the estimation of the min-conditional entropy. The entropic uncertainty principle lets one to take in account the information which is shared between multiple parties holding a multipartite quantum system and, more importantly, lets one to bound the information a party has on the system state after that it has been measured. We adapted such principle to the bipartite case where an user Alice, A, is supplied with a quantum system prepared by the provider Eve, E, who could be maliciously correlated to it. In principle then Eve might be able to predict all the outcomes of the measurements Alice performs on the basis Z in order to extract random numbers from the system. However we will show that if Alice randomly switches from the measurement basis to a basis X mutually unbiased to Z, she can lower bound the min entropy conditioned to the side information of Eve. In this way for Alice is possible to expand a small initial random seed in a much larger amount of trusted numbers. We present the results of an experimental demonstration of the protocol where random numbers passing the most rigorous classical tests of randomness were produced. In Chapter 6, we will provide a secure generation scheme for a continuos variable (CV) QRNG. Since random true random numbers are an invaluable resource for both the classical Information Technology and the uprising Quantum one, it is clear that to sustain the present and future even growing fluxes of data to encrypt it is necessary to devise quantum random number generators able to generate numbers in the rate of Gigabit or Terabit per second. In the Literature are given several examples of QRNG protocols which in theory could reach such limits. Typically, these are based on the exploitation of the quadratures of the electro-magnetic field, regarded as an infinite bosonic quantum system. The quadratures of the field can be measured with a well known measurement scheme, the so called homodyne detection scheme which, in principle, can yield an infinite band noise. Consequently the band of the random signal is limited only by the passband of the devices used to measure it. Photodiodes detectors work commonly in the GHz band, so if one sample the signal with an ADC enough fast, the Gigabit or Terabit rates can be easily reached. However, as in the case of discrete variable QRNG, the protocols that one can find in the Literature, do not properly consider the purity of the quantum state being measured. The idea has been to extend the discrete variable protocol of the previous Chapter, to the Continuous case. We will show how in the CV framework, not only the problem of the state purity is given but also the problem related to the precision of the measurements used to extract the randomness.
L'argomento di questa tesi può essere riassunto nella frase utilizzare il rumore classico per generare un migliore rumore quantistico. In particolare questa tesi riguarda da una parte la possibilita di sfruttare il rumore classico per trasmettere in modo efficace informazione quantistica, e dall'altra la misurazione del rumore classico per generare una migliore casualita quantistica. Nel primo caso ci si riferisce all'inviare bit quantistici attraverso l'atmosfera per creare trasmissioni allo scopo di distribuire chiavi crittografiche in modo quantistico (QKD) e questo sara oggetto di Capitolo 1 e Capitolo 2. Nel quadro delle comunicazioni quantistiche, la QKD è caratterizzata da notevoli difficolta sperimentali. Infatti, in linea di principio la QKD offre sicurezza incondizionata ma le sue realizzazioni pratiche devono affrontare tutti i limiti del mondo reale. Uno dei limiti principali sono le perdite introdotte dai canali di trasmissione. Le perdite causano errori e gli errori rendono il protocollo meno sicuro perché un avversario potrebbe camuffare la sua attivita di intercettazione utilizzando le perdite. Quando questo problema viene affrontato da un punto di vista teorico, si cerca di modellare l'effetto delle perdite mediante trasformazioni unitarie che trasformano i qubits in media secondo un livello fisso di attenuazione del canale. Tuttavia questo approccio è in qualche modo limitante, perché se si ha ha un elevato livello di rumore di fondo e le perdite si assumono costanti in media, potrebbe accadere che il protocollo possa abortire o peggio ancora, non iniziare, essendo il quantum bit error rate (QBER) oltre il limite (11\%) per la distribuzione sicura. Tuttavia, studiando e caratterizzando un canale ottico libero, si trova che il livello di perdite è tutt'altro che stabile e che la turbolenza induce variazioni di trasmissivita che seguono una statistica log-normale. Il punto pertanto è sfruttare questo rumore classico per generare chiave anche quando normalmente non sarebbe possibile. Per far ciò abbiamo ideato uno schema adattativo per la selezione in tempo reale (ARTS) degli istanti a basse perdite in cui vengono istantaneamente rilevati picchi di alta trasmissivita. A tal scopo, si utilizza un fascio laser classico ausiliario co-propagantesi con i qubit ma convenientemente inframezzato nel tempo. In questo modo la scintillazione viene monitorata in tempo reale e vengono selezionati gli intervalli di tempo che daranno luogo ad un QBER praticabile per una generazione di chiavi. Verra quindi presentato un criterio utile per la preselezione dell'intervallo di QBER basso in cui un treno di impulsi intensi si propaga nello stesso percorso dei qubits, con i parametri scelti in modo tale che la sua oscillazione nel tempo riproduce quello della comunicazione quantistica. Nel Capitolo 2 presentiamo quindi una dimostrazione ed i risultati di tale protocollo che è stato implementato presso l'arcipelago delle Canarie, tra l'isola di La Palma e quella di Tenerife: tali isole essendo separate da 143 km, costituiscono un ottimo teatro per testare la validita del protocollo in quanto le condizioni di distanza sono paragonabili a quelle satellitari e la gamma di scintillazione corrisponde quella che si avrebbe in ambiente con moderato maltempo in uno scenario di tipo urbano. Per quanto riguarda il contenuto del Capitolo 3 descriveremo un metodo innovativo per la generazione fisica di numeri casuali che si basa sulla constatazione che un fascio di luce coerente, attraversando un lungo percorso con turbolenza atmosferica da luogo ad immagini casuali e rapidamente variabili. Tale fenomeno è stato riscontrato a partire dai diversi esperimenti di comunicazione quantistica effettuati alle Isole Canarie, dove il fascio laser classico utilizzato per puntare i terminali, in fase di ricezione presentava un fronte d'onda completamente distorto rispetto al tipico profilo gaussiano. In particolare ciò che si osserva è un insieme di macchie chiare e scure che si evolvono geometricamente in modo casuale, il cosiddetto profilo dinamico a speckle. La fonte di tale entropia è quindi la turbolenza atmosferica. Infatti, per un canale di tale lunghezza, una soluzione delle equazioni di Navier-Stokes per il flusso atmosferico in cui si propaga il fascio è completamente fuori portata, sia analiticamente che per mezzo di metodi computazionali. Infatti i vari modelli di dinamica atmosferica sono basati sulla teoria statistica Kolmogorov, che parametrizza la ripartizione dell'energia cinetica come l'interazione di vortici d'aria di dimensioni decrescenti. Tuttavia, tali modelli forniscono solo una descrizione statistica per lo spot del fascio e delle sue eventuali deviazioni ma mai una previsione istantanea per la distribuzione dell' irraggiamento. Per tale motivo, quando un raggio laser viene inviato attraverso l'atmosfera, quest'ultima può essere considerato come un diffusore volumetrico dinamico che distorce il fronte d'onda del fascio. All'interno del Capitolo verranno presentati i dati sperimentali che assicurano che le immagini del fascio presentano le caratteristiche di impredicibilita tali per cui sia possibile numeri casuali genuini. Inoltre, verra presentato anche il metodo per l'estrazione della casualita basato sull'analisi combinatoria ed ottimale nel contesto della Teoria dell'Informazione. In Capitolo 5 presenteremo un nuovo approccio per quanto riguarda la generazione di bit casuali dai processi fisici quantistici. La Meccanica quantistica è stata sempre considerata come la migliore fonte di casualita, a causa della sua intrinseca natura probabilistica. Tuttavia il paradigma tipico impiegato per estrarre numeri casuali da un sistema quantistico assume che lo stato di detto sistema sia puro. Tale assunzione, in principio comporta una generazione in cui il risultato delle misure è complemente impredicibile secondo la legge di Born. Il problema principale tuttavia è che nelle implementazioni reali, come in un laboratorio o in qualche dispositivo commerciale, difficilmente è possibile creare uno stato quantico puro. Generalmente ciò che si ottiene è uno stato quantistico misto. Uno stato misto tuttavia potrebbe essere in qualche modo correlato con un altro sistema quantistico in possesso, eventualmente, di un avversario. Nel caso estremo di uno stato completamente misto, un generatore quantistico praticamente è equivalente ad un generatore che impiega un processo di fisica classica, che in principio è predicibile. Nel Capitolo, si mostrera quindi come sia necessario passare da un estimatore di casualita classico, come l' entropia minima classica $ H_ {min (Z) $ di una variabile casuale $ Z $ ad un estimatore che tenga conto di una informazione marginale $E$ di tipo quantistico, ovvero l'entropia minima condizionata $H_{min(Z|E)$. La entropia minima condizionata è una quantita fondamentale perchè consente di derivare quale sia il minimo contenuto di bit casuali estraibili dal sistema, in presenza di uno stato non puro. Abbiamo ideato un protocollo efficace basato sul principio di indeterminazione entropica per la stima dell'entropia min-condizionale. In generale, il principio di indeterminazione entropico consente di prendere in considerazione le informazioni che sono condivise tra più parti in possesso di un sistema quantistico tri-partitico e, soprattutto, consente di stimare il limite all'informazione che un partito ha sullo stato del sistema, dopo che è stato misurato. Abbiamo adattato tale principio al caso bipartito in cui un utente Alice, $A$, è dotato di un sistema quantistico che nel caso in studio ipotizziamo essere preparato dall'avversario stesso, Eve $E$, e che quindi potrebbe essere con esso correlato. Quindi, teoricamente Eve potrebbe essere in grado di prevedere tutti i risultati delle misurazioni che Alice esegue sulla sua parte di sistema, cioè potrebbe avere una conoscenza massima della variabile casuale $Z$ in cui si registrano i risultati delle misure nella base $\mathcal{Z$. Tuttavia mostreremo che se Alice casualmente misura il sistema in una base $\mathcal{X$ massimamente complementare a $\mathcal{Z$, Alice può inferire un limite inferiore l'entropia per $H_{min(Z|E)$. In questo modo per Alice, utilizzando tecniche della crittografia classeica, è possibile espandere un piccolo seme iniziale di casualita utilizzato per la scelta delle basi di misura, in una quantita molto maggiore di numeri sicuri. Presenteremo i risultati di una dimostrazione sperimentale del protocollo in cui sono stati prodotti numeri casuali che passano i più rigorosi test per la valutazione della casualita. Nel Capitolo 6, verra illustrato un sistema di generazione ultraveloce di numeri casuali per mezzo di variabili continue(CV) QRNG. Siccome numeri casuali genuini sono una preziosa risorsa sia per l'Information Technology classica che quella quantistica, è chiaro che per sostenere i flussi sempre crescenti di dati per la crittografia, è necessario mettere a punto generatori in grado di produrre streaming con rate da Gigabit o Terabit al secondo. In Letteratura sono riportati alcuni esempi di protocolli QRNG che potrebbero raggiungere tali limiti. In genere, questi si basano sulla misura dele quadrature del campo elettromagnetico che può essere considerato come un infinito sistema quantistico bosonico. Le quadrature del campo possono essere misurate con il cosiddetto sistema di rivelazione a omodina che, in linea di principio, può estrarre un segnale di rumore a banda infinita. Di conseguenza, la banda del segnale casuale viene ad essere limitata solo dalla banda passante dei dispositivi utilizzati per misurare. Siccome, rilevatori a fotodiodi lavorano comunemente nella banda delle decine dei GHz, se il segnale è campionato con un ADC sufficientemente veloce e con un elevato numero di bit di digitalizzazione, rate da Gigabit o Terabit sono facilmente raggiungibili. Tuttavia, come nel caso dei QRNG a variabili discrete, i protocolli che si hanno in Letteratura, non considerano adeguatamente la purezza dello stato quantistico da misurare. Nel L'idea è di estendere il protocollo a variabile discreta del capitolo precedente, al caso continuo. Mostreremo come nell'ambito CV, non solo sia abbia il problema della purezza dello stato ma anche il problema relativo alla precisione delle misure utilizzate su di esso. Proporremo e daremo i risultati sperimentali per un nuovo protocollo in grado di estrarre numeri casuali ad alto rate e con un elevato grado di sicurezza.

This dissertation formulates and applies a theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse variations. The resonance fluorescence spectrum in a high finesse optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Our analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular we determine a quantum limit to the semiclassical theory of FM modulation spectroscopy. Finally, we derive the corresponding theory for the two-photon, two-level medium. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem. We discuss the role of the Stark shifts on the emission spectrum and show how the Rayleigh scattering is markedly different.

A universal, scalable quantum computer will require the use of quantum error correction in order to achieve fault tolerance. The assessment and comparison of error-correcting strategies is performed by classical simulation. However, due to the prohibitive exponential scaling of general quantum circuits, simulations are restrained to specific subsets of quantum operations. This creates a gap between accuracy and efficiency which is particularly problematic when modeling noise, because most realistic noise models are not efficiently simulable on a classical computer. We have introduced extensions to the Pauli channel, the traditional error channel employed to model noise in simulations of quantum circuits. These expanded error channels are still computationally tractable to simulate, but result in more accurate approximations to realistic error channels at the single qubit level. Using the Steane [[7,1,3]] code, we have also investigated the behavior of these expanded channels at the logical error-corrected level. We have found that it depends strongly on whether the error is incoherent or coherent. In general, the Pauli channel will be an excellent approximation to incoherent channels, but an unsatisfactory one for coherent channels, especially because it severely underestimates the magnitude of the error. Finally, we also studied the honesty and accuracy of the expanded channels at the logical level. Our results suggest that these measures can be employed to generate lower and upper bounds to a quantum code's threshold under the influence of a specific error channel.

In this thesis we study the noise in Coulomb blockaded quantum dots in the vicinity of the peak of conductance in a full quantum treatment using the Keldysh technique. In previous work on this system, the emphasis have been on master equation approaches in the shot noise regime. In the vicinity of the peak of conductance it remained unclear if this classical approach is valid since we have two strongly interacting charging states and a full quantum treatment is necessary. Using our full, quantum mechanical approach we find an analytical expression for the noise valid from the low bias regime all the way to the shot noise regime valid in the vicinity of peak of conductance. In the shot noise regime we recover the result from the master equation approach.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.
Includes bibliographical references (leaves 137-144).
by Keren Bergman.
Ph.D.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, June 2004.
Includes bibliographical references (p. 89-91).
Quantum bang-bang control is a method of suppressing decoherence in qubits [VKL99, VL98]. To date, mathematically rigorous treatments of quantum bang-bang control offered little intuition. To complement existing approaches and to seek better understanding, I present intuitive pictures to think about quantum bang-bang control. In addition, I develop a formalism for treating phase noise moments of a qubit under quantum bang-bang control. Although the desired purpose of quantum bang-bang control is to remove noise, it is conceivable that it can be used to infer information about the noise process and coupling on a qubit. By using a simple random rotation model of single qubit dephasing, I demonstrate how quantum bang-bang control can distinguish between dephasing under different stochastic processes. I also show how quantum bang-bang control can determine noise coupling in a toy model where noise couples to the qubit via a fixed noise axis. These two demonstrations indicate the potential of quantum bang-bang control as a tool for qubit noise spectroscopy.
by Zilong Chen.
S.B.

Lateral semiconductor quantum dot structures have been proposed as an effective quantum bit (qubit) for quantum computation. A single excess electron with the freedom to move between two capacitively coupled quantum dots creates a `pseudo'-spin system with the same qubit behavior as the more natural two level system of a single electron spin. The excess electron in the double dot system is restricted to one of the two dots, thereby creating two separate and distinct states (usually referred to as |L> and |R>). The benefit of these charge qubits lie in the relative ease with which they can be manipulated and created. Experiments have been performed in this area and have shown controllable coherent oscillations and thus efficient single-qubit operations. However, the decoherence rates observed in the experiments is still quite high, making double dot charge qubits not very appealing for large-scale implementations. The following work describes the effect of the electromagnetic (EM) environment of the double quantum dot system on the decoherence of the charge state. Sources of decoherence in similar systems have been extensively investigated before and this paper follows a close theoretical framework to previous work done in the area. The effect of the EM environment can been seen in the calculations discussed below, although it is clear that the decoherence seen in experiments cannot be fully explained by the voltage fluctuations as they are investigated here. The limitations of the calculations are discussed and improvements are suggested.
M.S.
Department of Physics
Sciences
Physics

The research contained within this thesis concerns the detection, identification and effect of charge noise on quantum dot systems. In the first research chapter we study the cross correlation between pairs of exciton qubits subject to a common fluctuating charge environment, whose dynamics are solved using a transfer matrix approach. Our results show that we are able to discern features showing whether or not the charges interact with both quantum dots simultaneously i.e., form a correlated noise source. We find that qubits in a common charge environment display photon bunching, if both dots are driven on resonance or if the laser detunings are equal in both qubits and anitibunching if the laser detunings are in opposite directions. In the second research chapter we study the auto-correlation function of a single optically driven exciton qubit interacting with an environment consisting of 1/f noise and a fluctuating charge. We again use the transfer matrix method and a sum of Lorentzian distributions to approximate 1/f noise. Our simulations show that signatures of 1/f noise do exist in photon correlation measurements. From such measurements we are also able to determine a minimum cut-off frequency of the 1/f noise, in the case that there is such a cut-off. In addition we also show that a 1/f and a single fluctuator can be distinguished using the auto-correlation. In the final research chapter we study a pair of quantum dots, each with a low lying electron spin qubit and one higher lying level that can be selectively optically excited from one of the two spin states. Entanglement between the two spins can be achieved through path erasure. We look at the effect of a single fluctuating charge of the entanglement between these two `L' shaped electronic structures.

Photons provide low-noise quantum systems which are ideal for the fundamental studies of the quantum world and for developing new quantum technologies which promise to transform the way we process, transmit and acquire information. The development of the eld of quantum information processing, broadly dened, represents one of the most important scientic and technical challenges of the 21st Century. Photons have been used in demonstrations of basic quantum logic, secure communication tasks, precision measurements and the fundamental studies of quantum mechanics. In order to apply these systems and technologies in an ever increasing scale, it is necessary to develop new methods for eciently manipulating the quantum state of light. This is one of the main goals of this study which experimentally demonstrates new techniques for realising multi-qubit logic gates as well as a new method for amplifying quantum states of light noiselessly.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Natural Sciences
Science, Environment, Engineering and Technology
Full Text

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 35).
Craig Hogan recently proposed a "quantum holographic" noise that could potentially raise the expected noise floor for some current and upcoming high precision interferometers. Rainer Weiss et al. have designed an experiment searching for the noise in two coaligned Michelson interferometers. We have assembled and tested a photodetection system to measure broadband phase correlation between two optical signals, to be used in the noise detection experiment. This included modifying and characterizing photodetectors and setting up a system to record the signal correlation between the two detectors. We altered a LabVIEW program to assist in data collection and explored several ways to improve the data recording rate, which will allow larger data sets and thus longer runs. The detection system had a shot noise limited sensitivity of 4nV/vHz and allowed for measurements at the level of 1 % correlation.
by David Bruce Kelley.
S.B.

Kyoto University (京都大学)
0048
新制・課程博士
博士(理学)
甲第12076号
理博第2970号
新制||理||1444(附属図書館)
23912
UT51-2006-J71
京都大学大学院理学研究科物理学・宇宙物理学専攻
(主査)助教授 高橋 義朗, 教授 田中 耕一郎, 教授 松田 祐司
学位規則第4条第1項該当

The goal of research in quantum information is to investigate how quantum systems can be used to store, transmit and elaborate information and how the non-classical nature of their correlations allows defining protocols that outperform their classical counterparts. Despite of the many progresses, both theoretical and experimental, made in this field in the latest decades, many challenges lie ahead for practical implementations of quantum technologies. One of the most important ones is caused by the unavoidable interaction of quantum systems with their surroundings: The coupling to the environment is generally detrimental to the quantum information contained in the system as the system undergoes decoherence. In the quest for quantum technologies, it is fundamental to overcome the problem of decoherence and loss of information. Different physical implementations of qubits, such as superconducting and solid-state devices, are affected by the interaction with the environment in a way that can be described in terms of classical stochastic noise. The classical noise model can also be used to give an approximate, sometimes equivalent, description of full quantum models of system-environment interaction. This thesis contains my personal contribution to the study of the dynamics of discrete-variable quantum systems affected by classical noise. It covers in particular single- and two-qubit systems affected by Gaussian and non-Gaussian noise. It also discusses the dynamics of a quantum walk affected by spatially correlated classical noise. Analytical solutions for particular forms of noise and interactions, and a general numerical method for simulation of the dynamics are presented. Moreover, the thesis presents the experimental implementation of a quantum optical simulator of noisy dynamics of single-qubit systems. Finally, the use of quantum systems as probes of the spectral properties of large classical environments is discussed, showing that entanglement is a resource for improvements in the precision of the estimation.

The performance of optical measurement systems is ultimately limited by the quantum nature of light. In this thesis, two techniques for circumventing the standard quantum measurement limits are modelled and tested experimentally. These techniques are electro-optic control and the use of squeezed light. An optical parametric amplifier is used to generate squeezing at 1064nm. The parametric amplifier is pumped by the output of a second harmonic generation cavity, which in turn is pumped by a Nd:YAG laser. By using various frequency locking techniques, the quadrature phase of the squeezing is stabilised, therefore making our squeezed source suitable for long term measurements. The best recorded squeezing is 5.5dB (or 70\%) below the standard quantum limit. The stability of our experiment makes it possible to perform a time domain measurement of photocurrent correlations due to squeezing. This technique allows direct visualisation of the quantum correlations caused by squeezed light. On the road to developing our squeezed source, methods of frequency locking optical cavities are investigated. In particular, the tilt locking method is tested on the second harmonic generation cavity used in the squeezing experiment. The standard method for locking this cavity involves the use of modulation sidebands, therefore leading to a noisy second harmonic wave. The modulation free tilt-locking method, which is based on spatial mode interference, is shown to be a reliable alternative. In some cases, electro-optic control may be used to suppress quantum measurement noise. Electro-optic feedback is investigated as a method for suppressing radiation pressure noise in an optical cavity. Modelling shows that the `squashed' light inside a feedback loop can reduce radiation pressure noise by a factor of two below the standard quantum limit. This result in then applied to a thermal noise detection system. The reduction in radiation pressure noise is shown to give improved thermal noise sensitivity, therefore proving that the modified noise properties of light inside a feedback loop can be used to reduce quantum measurement noise. Another method of electro-optic control is electro-optic feedforward. This is also investigated as a technique for manipulating quantum measurements. It is used to achieve noiseless amplification of a phase quadrature signal. The results clearly show that a feedforward loop is a phase sensitive amplifier that breaks the quantum limit for phase insensitive amplification. This experiment is the first demonstration of noiseless phase quadrature amplification. Finally, feedforward is explored as a tool for improving the performance of quantum nondemolition measurements. Modelling shows that feedforward is an effective method of increasing signal transfer efficiency. Feedforward is also shown to work well in conjunction with meter squeezing. Together, meter squeezing and feedforward provide a comprehensive quantum nondemolition enhancement package. Using the squeezed light from our optical parametric amplifier, an experimental demonstration of the enhancement scheme is shown to achieve record signal transfer efficiency of $T_{s}+T_{m}=1.81$.

Gravitational waves are a predication of Einstein's theory of general relativity. After nearly 50 years of effort by the scientific community to construct a detector capable of directly measuring gravitational waves, we expect a breakthrough, the first ever direct measurement of a gravitational wave within the next 5 years. The Advanced LIGO detectors currently under construction are predicted to achieve not only the first detection but to open the field of gravitational-wave astronomy: as an observational window on astrophysics and with an impart on other areas such as cosmology, strong-field gravity, general relativity, and nuclear physics. The Advanced LIGO detectors are large-scale laser interferometers that have been designed for very low technical noise so that quantum noise will be limiting their sensitivity over a wide range of their spectrum. Planning for future gravitational wave observatories is already underway and reducing the fundamental quantum noise is considered to be one of the main experimental challenges. My work over the last 4 years has focused on possible new techniques to reduce or circumvent the quantum noise in laser interferometers.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.
Includes bibliographical references (p. 181-189).
In recent years, a variety of mechanical systems have been approaching quantum limits to their sensitivity of continuous position measurements imposed by the Heisenberg Uncertainty Principle. Most notably, gravitational wave interferometers, such as the Laser Interferometer Gravitational wave Observatory (LIGO), operate within a factor of 10 of the standard quantum limit. Here we characterize and manipulate quantum noise in a variety of alternative topologies which may lead to higher sensitivity GW detectors, and also provide an excellent testbed for fundamental quantum mechanics. Techniques considered include injection and generation of non-classical (squeezed) states of light, and cooling and trapping of macroscopic mirror degrees of freedom by manipulation of the optomechanical coupling between radiation pressure and mirror motion. A computational tool is developed to model complex optomechanical systems in which these effects arise. The simulation tool is used to design an apparatus capable of demonstrating a variety of radiation pressure effects, most notably ponderomotive squeezing and the optical spring effect. A series of experiments were performed, designed to approach measurement of these effects. The experiments use a 1 gram mirror to show progressively stronger radiation pressure effects, but only in the classical regime. The most significant result of these experiments is that we use radiation pressure from two" optical fields to shift the mechanical resonant frequency of a suspended mirror from 172 Hz to 1.8 kHz, while simultaneously damping its motion. The technique could prove useful in advanced gravitational wave interferometers by easing control issues, and also has the side effect of effectively cooling the mirror by removing its thermal energy. We show that with improvements, the technique may allow the quantum ground state of the mirror to be approached. Finally, we discuss future prospects for approaching quantum effects in the experiments.
by Thomas Randall Corbitt.
Ph.D.

The current network of three terrestrial interferometric gravitational wave detectors have observed ten binary black holes and one binary neutron star to date in the frequency band from 10 Hz to 5 kHz. Future detectors will increase the sensitivity by up to a factor of 10 and will push the sensitivity band down to lower frequencies. However, observing sources lower than a few Hz requires going into space where the interferometer arms can be longer and where there is no seismic noise. A new 100 km space detector, TianGO, sensitive to the frequency band from 10 mHz to 100 Hz is described. Through its excellent ability to localize sources in the sky, TianGO can use binary black holes as standard candles to help resolve the current tension between measurements of the Hubble constant. Furthermore, all of the current and future detectors, on both the ground and in space, are limited by quantum shot noise at high frequencies, and some will be limited by quantum radiation pressure at low frequencies as well. Much effort is made to use squeezed states of light to reduce this quantum noise, however classical noise and losses severely limit this reduction. One would ideally design a gravitational wave transducer that, using its own ability to generate ponderomotive squeezing due to the radiation pressure mediated interaction between the optical modes of the light and the mechanical modes of the mirrors, approaches the fundamental limits to quantum measurement. First steps in this direction are described and it is shown that it is feasible that a large scale 40 m interferometer can observe this ponderomotive squeezing in the near future. Finally, a method of removing the effects of the vacuum fluctuations responsible for the quantum noise in gravitational wave detectors and its application to testing for the presence of deviations from general relativity is described.

For quantum computers to reach their full potential will require error correction. We study the surface code, one of the most promising quantum error correcting codes, in the context of predominantly dephasing (Z-biased) noise, as found in many quantum architectures. We find that the surface code is highly resilient to Y-biased noise, and tailor it to Z-biased noise, whilst retaining its practical features. We demonstrate ultrahigh thresholds for the tailored surface code: ~39% with a realistic bias of  = 100, and ~50% with pure Z noise, far exceeding known thresholds for the standard surface code: ~11% with pure Z noise, and ~19% with depolarizing noise. Furthermore, we provide strong evidence that the threshold of the tailored surface code tracks the hashing bound for all biases. We reveal the hidden structure of the tailored surface code with pure Z noise that is responsible for these ultrahigh thresholds. As a consequence, we prove that its threshold with pure Z noise is 50%, and we show that its distance to Z errors, and the number of failure modes, can be tuned by modifying its boundary. For codes with appropriately modified boundaries, the distance to Z errors is O(n) compared to O(n1/2) for square codes, where n is the number of physical qubits. We demonstrate that these characteristics yield a significant improvement in logical error rate with pure Z and Z-biased noise. Finally, we introduce an efficient approach to decoding that exploits code symmetries with respect to a given noise model, and extends readily to the fault-tolerant context, where measurements are unreliable. We use this approach to define a decoder for the tailored surface code with Z-biased noise. Although the decoder is suboptimal, we observe exceptionally high fault-tolerant thresholds of ~5% with bias  = 100 and exceeding 6% with pure Z noise. Our results open up many avenues of research and, recent developments in bias-preserving gates, highlight their direct relevance to experiment.

La métrologie de haute précision est une application des peignes de fréquences optiques. Typiquement, la sensibilité de mesure est limitée par le bruit classique des propriétés des peignes. Leur bruit d'amplitude et de phase a été largement étudié et jusqu'à présent. Pourtant, uniquement des bandes latérales de bruit proche de la porteuse ont été caractérisées pour des fréquences individuelles et le champs moyen.Cette thèse développe des méthodes de caractérisation de bruit d'amplitude et phase à la limite quantique. A cette fin, une cavité passive et large bande est développée. Elle filtre et inter-convertit les bruits d'amplitude et phase. L'analyse de son signal à l'aide d'une détection homodyne permet la mesure du bruit de phase avec une sensibilité à la limite quantique. L'application d'un façonnage des impulsions ultra brèves rend possible la mesure des corrélations spectrales du bruit. Tout en étant représentés par des matrices de covariance, l'ensemble des corrélations du bruit sur le spectre optique d'un oscillateur Ti:Sapph est caractérisé.Les corrélations mesurées montrent des structures spectrales, dites " modes ", qui sont en accord avec la prédiction théorique. Ce concept apparait comme analogue au formalisme décrivant des systèmes multi-partites en optique quantique. Il est par conséquent aussi un moyen de description de bruit classique. La connaissance des modes intrinsèques du bruit est susceptible de mener à une amélioration de la précision de mesures avec des peignes de fréquences optiques
Precision metrology is one application of optical frequency combs. Classical noise in their properties typically limits achievable measurement sensitivity. Amplitude and phase noise in optical frequency combs have already been studied extensively. So far, noise sidebands close to the carrier of either individual optical frequencies or of the mean field were considered. This thesis develops methods to precisely characterize amplitude and phase noise down to the quantum limit. To this aim a transmissive, broadband passive cavity is developed. It filters and inter-converts amplitude and phase noise. The analysis of its signal by the use of homodyne detection provides a quantum limited measurement of phase noise. The application of ultrafast pulse shaping enables the measurement of the spectral correlations of amplitude and phase noise. Being represented by the use of covariance matrices, the entire noise correlations over the optical spectrum are characterized on the example of a Ti:Sapph oscillator. The measured noise correlations exhibit spectral structures, so-called “modes”. Their shape matches with the theoretical prediction. This concept known from multi-partite optical quantum systems is consequently applicable to classical noise in frequency combs. The knowledge of the intrinsic noise modes is likely provide an improvement of precision metrology experiments with combs