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The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum “supremacy"). In this work, we investigate whether quantum advantage demonstrations can be achieved for more physically-motivated sampling problems, related to measurements of physical observables. We focus on the problem of sampling the outcomes of an energy measurement, performed on a simple-to-prepare product quantum state – a problem we refer to as energy sampling. For different regimes of measurement resolution and measurement errors, we provide complexity theoretic arguments showing that the existence of efficient classical algorithms for energy sampling is unlikely. In particular, we describe a family of Hamiltonians with nearest-neighbour interactions on a 2D lattice that can be efficiently measured with high resolution using a quantum circuit of commuting gates (IQP circuit), whereas an efficient classical simulation of this process should be impossible. In this high resolution regime, which can only be achieved for Hamiltonians that can be exponentially fast-forwarded, it is possible to use current theoretical tools tying quantum advantage statements to a polynomial-hierarchy collapse whereas for lower resolution measurements such arguments fail. Nevertheless, we show that efficient classical algorithms for low-resolution energy sampling can still be ruled out if we assume that quantum computers are strictly more powerful than classical ones. We believe our work brings a new perspective to the problem of demonstrating quantum advantage and leads to interesting new questions in Hamiltonian complexity., SCOPUS: ar.j, info:eu-repo/semantics/published

As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS-in the form of an inequality between the input squeezing parameter, the overall transmission rate, and the quality of photon detectors. Our result serves as a nonclassicality test that must be passed by any quantum computational supremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss., SCOPUS: ar.j, DecretOANoAutActif, info:eu-repo/semantics/published

Boson sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of 'quantum computational supremacy', this motivates optimising classical simulation schemes for a realistic model of the problem, in this case boson sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of boson sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised boson sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches., SCOPUS: ar.j, DecretOANoAutActif, info:eu-repo/semantics/published

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The aim of this thesis is the introduction of new practical Quantum Random Number Generators and new mathematical techniques to certify the random nature of the numbers, based only on a partial characterisation of the devices. Random numbers have a lot of applications, going from mathematical algorithms and betting games to cryptographic protocols, where random keys are a basic premise for constructing protocols. Random Number Generators of the Quantum type have the advantage that they rely on truly random processes, which are guaranteed to be unpredictable by the laws of physics. This makes them in principle more safe than classical hardware generators and pseudo-random algorithms. In the first part of the thesis, we focus of the task of certifying randomness. We introduce a new framework for certifying generators based on quantum optics and that follow a Prepare-and-Measure setup consisting of a source and a measurement device, such as a laser and a single photon detector. Our framework is called semi-Device-Independent, because the device is left largely uncharacterised, as no assumption is made on the source and the measurement device, except for a single physical assumption on the mean photon number (or the energy) of the states prepared by the source. This approach is very secure and robust because any malfunctioning or imperfections in the generator, such additional classical noise, are automatically taken into account as long as the energy assumption is satisfied. We show that, under an energy constraint, there is a fundamental relation between the amount of correlation between the two devices and the amount of randomness produced during the measurement. We establish this by considering all possible underlying quantum models of the devices, that satisfy the mean photon number constraint. We demonstrate that certain strong correlations indeed cannot be reproduced by an underlying deterministic model and show how to compute the amount of randomness in these ca, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Photon losses are among the strongest imperfections affecting multi-photon interference. Despite their importance, little is known about their effect on boson sampling experiments. In this work we show that using classical computers, one can efficiently simulate multi-photon interference in all architectures that suffer from an exponential decay of the transmission with the depth of the circuit, such as integrated photonic circuits or optical fibers. We prove that either the depth of the circuit is large enough that it can be simulated by thermal noise with an algorithm running in polynomial time, or it is shallow enough that a tensor network simulation runs in quasi-polynomial time. This result suggests that in order to implement a quantum advantage experiment with single-photons and linear optics new experimental platforms may be needed., SCOPUS: ar.j, info:eu-repo/semantics/published

The symplectic formalism applied to the phase-space representation of bosonic quantum systems provides us with a powerful mathematical tool for the characterisation of Gaussian states and transformations. As a consequence, quantum information protocols involving the latter are very well understood from a theoretical point of view. Nevertheless, it has become clear in recent years that the use of non-Gaussian resources is necessary in order to perform various crucial information-processing tasks. An illustration of this fact can for instance be found in situations where a Gaussian no-go theorem precludes the use of Gaussian transformations in order to achieve a task involving Gaussian states, such as quantum entanglement distillation, quantum error correction, or universal quantum computation. In the first part of this thesis, we develop a new method based on the generating function of a sequence, which gives rise to an elegant description of intrinsically non-Gaussian objects. Building on the generating function of the matrix elements of Gaussian unitaries in Fock basis, our approach gives access to the multi-photon transition probabilities via unexpectedly simple recurrence equations. The method is developed for Gaussian unitaries effecting both passive and active linear coupling between two bosonic modes. It predicts an interferometric suppression term which generalises the Hong-Ou-Mandel effect for more than two indistinguishable photons impinging on a balanced beam splitter. Furthermore, it exhibits an unsuspected 2-photon suppression effect in optical parametric amplification of gain 2, which originates from the indistinguishability between the input and output photon pairs. Finally, we extend our method to Bogoliubov transformations acting on an arbitrary number of modes. In the second part of this thesis, we introduce a class of Gaussian-dilatable bosonic quantum channels (characterised by a Gaussian unitary in their Stinespring dilation) called passive-envir, Le formalisme symplectique appliqué à la représentation des systèmes bosoniques dans l'espace des phases donne accès à un outil mathématique puissant pour la caractérisation des états gau-ssiens et transformations gaussiennes. Les protocoles d'information quantique impliquant ces derniers sont d'ailleurs très bien compris d'un point de vue théorique. Toutefois, il s'est avéré clair durant ces dernières années que l'utilisation de ressources non-gaussiennes est nécessaire afin d'effectuer des tâches cruciales de traitement de l'information. En effet, certaines tâches — telles que la distillation d’intrication quantique, le codage quantique ou encore le calcul quantique — impliquant des états gaussiens ne peuvent être effectuées avec des transformations gaussiennes. Dans la première partie de cette thèse, nous développons une nouvelle méthode basée sur la fonction génératrice d'une suite qui donne lieu à une description élégante d'objets intrinsèquement non-gaussiens. Se basant sur la fonction génératrice des éléments de matrice d'unitaires gaussiens dans la base de Fock, notre approche donne accès aux probabilités de transition multi-photon via des équations de récurrence étonnamment simples. La méthode est développée pour des unitaires gaussiens produisant des couplages linéaires passifs et actifs entres deux modes bosoniques. Elle prédit un terme d'interférence destructive qui généralise l'effet Hong-Ou-Mandel pour plus de deux photons indistinguables pénétrant dans un diviseur de faisceau équilibré. De plus, elle met en évidence un effet inattendu de suppression de deux photons dans un amplificateur paramétrique optique de gain 2. Cette suppression résulte de l’indistinguabilité entre les paires de photons d’entrée et de sortie. Finalement, nous étendons notre méthode à des transformations de Bogoliubov agissant sur un nombre de modes arbitraire. Dans la seconde partie de cette thèse, nous introduisons une classe de canaux quantiques bosoniques gaussiens-dilatable, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

The capability of a given channel to communicate information is, a priori, distinct from its capability to distribute shared randomness. In this paper, we define randomness distribution capacities of quantum channels assisted by forward, back, or two-way classical communication and compare these to the corresponding communication capacities. With forward assistance or no assistance, we find that they are equal. We establish the mutual information of the channel as an upper bound on the two-way assisted randomness distribution capacity. This implies that all of the capacities are equal for classical-quantum channels. On the other hand, we show that the back-assisted randomness distribution capacity of a quantum-classical channel is equal to its mutual information. This is often strictly greater than the back-assisted communication capacity. We give an explicit example of such a separation where the randomness distribution protocol is noiseless., SCOPUS: cp.j, info:eu-repo/semantics/published

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments., SCOPUS: ar.j, info:eu-repo/semantics/published

The generation of random number sequences, that is, of unpredictable sequences free from any structure, has found numerous applications in the field of information technologies. One of the most sensitive applications is cryptography, whose modern practice makes use of secret keys that must indeed be unpredictable for any potential adversary. This type of application demands highly secure randomness generators.This thesis contributes to the device-independent approach to quantum random number generation (DIRNG, for Device-Independent Random Number Generation). Those methods of randomness generation exploit the fundamental unpredictability of the measurement of quantum systems. In particular, the security of device-independent methods does not appeal to a specific model of the device itself, which is treated as a black box. This approach therefore stands in contrast to more traditional methods whose security rests on a precise theoretical model of the device, which may lead to vulnerabilities caused by hardware malfunctions or tampering by an adversary.Our contributions are the following. We first introduce a family of robust self-testing criteria for a class of quantum systems that involve partially entangled qubit pairs. This powerful form of inference allows us to certify that the contents of a quantum black box conforms to one of those systems, on the sole basis of macroscopically observable statistical properties of the black box.That result leads us to introduce and prove the security of a protocol for randomness generation based on such partially entangled black boxes. The advantage of this method resides in its low shared entanglement cost, which allows to reduce the use of quantum resources (both entanglement and quantum communication) compared to existing DIRNG protocols.We also present a protocol for randomness generation based on an original estimation of the black-box correlations. Contrary to existing DIRNG methods, which summarize the accumulated measur, La génération de suites de nombres aléatoires, c'est-à-dire de suites imprévisibles et dépourvues de toute structure, trouve de nombreuses applications dans le domaine des technologies de l'information. L'une des plus sensibles est la cryptographie, dont les pratiques modernes font en effet appel à des clés secrètes qui doivent précisément être imprévisibles du point de vue d'adversaires potentiels. Ce type d'application exige des générateurs d'aléa de haute sécurité.Cette thèse s'inscrit dans le cadre de l'approche indépendante des appareils des méthodes quantiques de génération de nombres aléatoires (en anglais, Device-Independent Random Number Generation ou DIRNG). Ces méthodes exploitent la nature fondamentalement imprévisible de la mesure des systèmes quantiques. En particulier, l'appellation "indépendante des appareils" implique que la sécurité de ces méthodes ne fait pas appel à un modèle théorique particulier de l'appareil lui-même, qui est traité comme une boîte noire. Cette approche se distingue donc de méthodes plus traditionnelles dont la sécurité repose sur un modèle théorique précis de l'appareil et peut donc être compromise par un dysfonctionnement matériel ou l'intervention d'un adversaire.Les contributions apportées sont les suivantes. Nous démontrons tout d'abord une famille de critères de "self-testing" robuste pour une classe de systèmes quantiques impliquant des paires de systèmes à deux niveaux (qubits) partiellement intriquées. Cette forme d'inférence particulièrement puissante permet de certifier que le contenu d'une boîte noire quantique est conforme à l'un de ces systèmes, sur base uniquement de propriétés statistiques de la boîte observables macroscopiquement.Ce résultat nous amène à introduire et à prouver la sécurité d'une méthode de génération d'aléa basée sur ces boîtes noires partiellement intriquées. L'intérêt de cette méthode réside dans son faible coût en intrication, qui permet de réduire l'usage de ressources quantiques (intricat, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes contain natural divergences since the maximally entangled state is ill defined. We introduce a method that avoids such divergences by utilizing finitely entangled (squeezed) states and then taking the limit of arbitrary large squeezing. Using this method, we derive an operator-sum representation for all single-mode bosonic Gaussian channels where a unique feature is that both quantum-limited and noisy channels are treated on an equal footing. This technique facilitates a proof that the rank-1 Kraus decomposition for Gaussian channels at its respective entanglement-breaking thresholds, obtained in the overcomplete coherent-state basis, is unique. The methods could have applications to simulation of continuous-variable channels., SCOPUS: ar.j, info:eu-repo/semantics/published

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We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development., SCOPUS: ar.j, info:eu-repo/semantics/published

Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy power inequality (EPI). We develop an axiomatic framework from which we deduce the natural form of a discrete-variable EPI and an associated entropic monotonicity in a discrete-variable central limit theorem. In this discrete EPI, the geometric distribution, which has the maximum entropy among all discrete distributions with a given mean, assumes a role analogous to the Gaussian distribution in Shannon's EPI. The entropy power of X is defined as the mean of a geometric random variable with entropy H(X). The crux of our construction is a discrete-variable version of Lieb's scaled addition X plusbη Y of two random variables X and Y with η ⋯ (0, 1). We discuss the relationship of our discrete EPI with recent work of Yu and Johnson who developed an EPI for a restricted class of random variables that have ultra-log-concave (ULC) distributions. Even though we leave open the proof of the aforesaid natural form of the discrete EPI, we show that this discrete EPI holds true for variables with arbitrary discrete distributions when the entropy power is redefined as eH(X) in analogy with the continuous version. Finally, we show that our conjectured discrete EPI is a special case of the yet-unproven Entropy Photon-number Inequality (EPnI), which assumes a role analogous to Shannon's EPI in capacity proofs for Gaussian bosonic (quantum) channels., SCOPUS: cp.p, info:eu-repo/semantics/published

It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics., SCOPUS: ar.j, info:eu-repo/semantics/published

BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this work, we investi- gate whether an experimentally realistic BosonSampler can really solve BosonSampling without any fault-tolerance mechanism. More precisely, we study how the unavoidable errors linked to an imperfect calibration of the optical elements affect the final result of the computation. We show that the fidelity of each optical element must be at least 1 -O(1=n2), where n refers to the number of single photons in the scheme. Such a requirement seems to be achievable with state-of-the-art equipment., SCOPUS: ar.j, info:eu-repo/semantics/published

We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke, Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other., SCOPUS: ar.j, info:eu-repo/semantics/published

The capability of a given channel to transmit information is, a priori, distinct from its capability to distribute random correlations. Despite that, for classical channels, the capacity to distribute information and randomness turns out to be the same, even with the assistance of auxiliary communication. In this work we show that this is no longer true for quantum channels when feedback is allowed. We prove this by constructing a channel that is noisy for the transmission of information but behaves as a virtual noiseless channel for randomness distribution when assisted by feedback communication. Our result can be seen as a way of unlocking quantum randomness internal to the channel., SCOPUS: cp.p, info:eu-repo/semantics/published

We establish the classical capacity of optical quantum channels as a sharp transition between two regimes - one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity. This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels, such as lossy optical fibers, amplifier, and free-space communication. The theorem holds under a particular photon-number occupation constraint, which we describe in detail in this paper. Our result bolsters the understanding of the classical capacity of these channels and opens the path to applications, such as proving the security of noisy quantum storage models of cryptography with optical links., SCOPUS: ar.j, info:eu-repo/semantics/published

The long-standing conjectures of the optimality of Gaussian inputs and additivity are solved for a broad class of gauge-covariant or contravariant bosonic Gaussian channels (which includes in particular thermal, additive classical noise, and amplifier channels) restricting to the class of states with finite second moments. We show that the vacuum is the input state which minimizes the entropy at the output of such channels. This allows us to show also that the classical capacity of these channels (under the input energy constraint) is additive and is achieved by Gaussian encodings., SCOPUS: ar.j, SCOPUS: ar.j, info:eu-repo/semantics/published

We prove that a strong converse theorem holds for the classical capacity of all phase-insensitive bosonic Gaussian channels, when imposing a maximum photon number constraint on the inputs of the channel. This class is a natural extension of classical continuous Gaussian channels, and the well studied pure-loss, thermal, additive noise, and amplifier channels are all in this class of channels. The statement of the strong converse theorem is that the probability of correctly decoding a classical message rapidly converges to zero in the limit of many channel uses if the communication rate exceeds the classical capacity. We prove this theorem by relating the success probability of any code with its rate of data transmission, the effective dimension of the channel output space, and the purity of the channel as quantified by the minimum output entropy. Our result bolsters the understanding of the classical capacity of these channels by establishing it as a sharp dividing line between possible and impossible communication rates over them. © 2014 IEEE., ISSN:2157-8095, info:eu-repo/semantics/published

Optical parametric amplifiers together with phase-shifters and beamsplitters have certainly been the most studied objects in the field of quantum optics. Despite such an intensive study, optical parametric amplifiers still keep secrets from us. We will show how they hold the answer to one of the oldest problems in quantum communication theory, namely the calculation of the optimal communication rate of optical channels., info:eu-repo/semantics/published

Optical channels, such as fibres or free-space links, are ubiquitous in today's telecommunication networks. They rely on the electromagnetic field associated with photons to carry information from one point to another in space. A complete physical model of these channels must necessarily take quantum effects into account to determine their ultimate performances. Single-mode, phase-insensitive bosonic Gaussian channels have been extensively studied over past decades, given their importance for practical applications. In spite of this, a long-standing unsolved conjecture on the optimality of Gaussian encodings has prevented finding their classical communication capacity. Here, this conjecture is solved by proving that the vacuum state achieves the minimum output entropy of these channels. This establishes the ultimate achievable bit rate under an energy constraint, as well as the long awaited proof that the single-letter classical capacity of these channels is additive., SCOPUS: ar.j, info:eu-repo/semantics/published

We prove the security of Gaussian continuous-variable quantum key distribution with coherent states against arbitrary attacks in the finite-size regime. In contrast to previously known proofs of principle (based on the de Finetti theorem), our result is applicable in the practically relevant finite-size regime. This is achieved using a novel proof approach, which exploits phase-space symmetries of the protocols as well as the postselection technique introduced by Christandl, Koenig, and Renner. © 2013 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

We prove the equivalence of an arbitrary single-mode Gaussian quantum channel and a newly defined fiducial channel preceded by a phase shift and followed by a Gaussian unitary operation. This equivalence implies that the energy-constrained classical capacity of any single-mode Gaussian channel can be calculated based on this fiducial channel, which is furthermore simply realizable with a beam splitter, two identical single-mode squeezers, and a two-mode squeezer. In a large domain of parameters, we also provide an analytical expression for the Gaussian classical capacity, exploiting its additivity, and prove that the classical capacity cannot exceed it by more than 1/ln2 bits., SCOPUS: ar.j, info:eu-repo/semantics/published

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments., Engineering and Physical Sciences Research Council (No. EP/J00796X/1), Future & Emerging Technologies (Program) (Grant No. 212008), European Union (No. MOIF-CT- 2006-039703), Belgian Science Policy Office (Grant No. IAP P6-10)

The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected., SCOPUS: ar.j, info:eu-repo/semantics/published

A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory., SCOPUS: ar.j, info:eu-repo/semantics/published

A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory., Alexander von Humboldt-Stiftung, Belgian National Foundation for Scientific Research, European Union (Project No. FIS2008-06024-C03-01), W. M. Keck Foundation Center for Extreme Quantum Information Theory, Spain. Ministerio de Ciencia e Innovación (MICINN) (FPU), United States. Office of Naval Research (Basic Research Challenge Program), Fondation pour la recherche strategique (France) (HIPERCOM)

The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected., Spain. Ministerio de Ciencia e Innovación (MICINN). FPU Program, W. M. Keck Foundation Center for Extreme Quantum Information Theory, Alexander von Humboldt-Stiftung, United States. Office of Naval Research. Basic Research Challenge Program, European Union. European Regional Development Fund (Project FIS2008-06024-C03-01), European Commission. Project MALICIA (Grant 265522)

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch’s theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation., W. M. Keck Foundation, Jeffrey Epstein, National Science Foundation (U.S.), United States. Office of Naval Research, United States. Defense Advanced Research Projects Agency, NEC Corporation Fund for Research in Computers and Communications

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch’s. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the “grandfather paradox” is resolved., National Science Foundation (U.S.), Natural Sciences and Engineering Research Council of Canada, United States. Defense Advanced Research Projects Agency, United States. Office of Naval Research, QuantumWorks Corporation, Canadian Institute for Advanced Research, National Institute of Standards and Technology (U.S.)

We propose the use of single-photon two-qubit quantum logic to physically simulate the optimal individual attack on Bennett-Brassard 1984 quantum key distribution protocol.The experimental setup does not require a quantum memory due to the physical simulation character of the proposal., W.M. Keck Foundation (Center for extreme Quantum Information Theory (xQIT))

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A continuous-variable quantum key distribution protocol based on squeezed states and heterodyne detection is introduced and shown to attain higher secret key rates over a noisy line than any other one-way Gaussian protocol. This increased resistance to channel noise can be understood as resulting from purposely adding noise to the signal that is converted into the secret key. This notion of noise-enhanced tolerance to noise also provides a better physical insight into the poorly understood discrepancies between the previously defined families of Gaussian protocols., W. M. Keck Foundation Center for Extreme Quantum Information Theory, FRIA, European Union SECOQC project, European Union COMPAS project

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In this Letter we define a family of entanglement distribution protocols assisted by feedback classical communication that gives an operational interpretation to reverse coherent information, i.e., the symmetric counterpart of the well-known coherent information. This leads to the definition of a new entanglement distribution capacity that exceeds the unassisted capacity for some interesting channels., W. M. Keck Foundation Center for Extreme Quantum Information Theory

We define the direct and reverse secret-key capacities of a memoryless quantum channel as the optimal rates that entanglement-based quantum-key-distribution protocols can reach by using a single forward classical communication (direct reconciliation) or a single feedback classical communication (reverse reconciliation). In particular, the reverse secret-key capacity can be positive for antidegradable channels, where no forward strategy is known to be secure. This property is explicitly shown in the continuous variable framework by considering arbitrary one-mode Gaussian channels., 6th European Community Framework Programme - Marie Curie Action, W. M. Keck Foundation Center for Extreme Quantum Information Theory

A continuous-variable quantum key distribution protocol based on squeezed states and heterodyne detection is introduced and shown to attain higher secret key rates over a noisy line than any other one-way Gaussian protocol. This increased resistance to channel noise can be understood as resulting from purposely adding noise to the signal that is converted into the secret key. This notion of noise-enhanced tolerance to noise also provides a better physical insight into the poorly understood discrepancies between the previously defined families of Gaussian protocols., Journal Article, info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

In this thesis we have studied different aspects of the novel field of quantum information with continuous variables. The higher efficiency and bandwidth of homodyne detection combined with the easiness of generation and manipulation of Gaussian states makes continuous-variable quantum information a promising and flourishing field of research. This dissertation is divided in two parts. The first part explores two applications of the “photon subtraction” operation; Firstly, a technique to generate highly non-Gaussian single-mode states of light; Secondly, an experimental setup capable of realizing a loophole-free Bell test. The second part of this dissertation develops a detailed analysis of an important family of continuous-variable quantum key distribution protocols, namely those based on Gaussian modulation of Gaussian states./Dans cette thèse on a étudié différents aspects de l'information quantique à variables continues. Les meilleures efficacité et bande passante de la détection homodyne combinées à la simplicité de génération et de manipulation d'états gaussiens rend l'information quantique à variables continues un domaine de recherche très prometteur, qui est actuellement en plein essor. La dissertation est divisée en deux parties. La première explore deux applications de l'opération “soustraction de photon”; en premier lieu on présente une nouvelle technique capable de générer des états mono-modaux de la lumière hautement non-gaussiens; deuxiemement on présente un schéma expérimental capable de réaliser un test de Bell sans faille logique. La deuxième partie de cette dissertation développe une étude détaillée d'une famille très importante de protocoles de distribution quantique de clé à variables continues, ceux basés sur la modulation gaussienne d'états gaussiens., Doctorat en Sciences de l'ingénieur, info:eu-repo/semantics/nonPublished

It is shown that a loophole-free Bell test can be achieved using continuous variables of light. A feasible optical setup is proposed for this purpose, based on a non-Gaussian state of light and high-efficiency homodyne detectors. The non-Gaussian entangled state can be generated from a two-mode squeezed vacuum state by subtracting a single photon from each mode using beam splitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% can be attained with 6 dB squeezed light and an homodyne efficiency around 95%. A detailed feasibility analysis, including the effect of the detector efficiency, the electronic noise, the impurity of the non-Gaussian state, and the probability of false triggers, suggests that this method opens a promising avenue towards a complete experimental Bell test., SCOPUS: ch.b, info:eu-repo/semantics/published