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The application of a mechanical strain to a 2D material can create pseudo-magnetic fields and lead to a quantized valley Hall effect. However, measuring valley-resolved effects remains a challenging task due to their inherent fragility and dependence on the sample’s proper design. Additionally, non-local transport probes based on multiterminal devices have often proven to be inadequate in yielding conclusive evidence of the valley Hall signal. Here, we introduce an alternative way of detecting the quantized valley Hall effect, which entirely relies on local density measurements, performed deep in the bulk of the sample. The resulting quantized signal is a genuine Fermi sea response, independent of the edge physics, and reflects the underlying valley Hall effect through the Widom-Středa formula. Specifically, our approach is based on measuring the variation of the particle density, locally in the bulk, upon varying the strength of the applied strain. This approach to the quantized valley Hall effect is particularly well suited for experiments based on synthetic lattices, where the particle density (or integrated density of states) can be spatially resolved., SCOPUS: ar.j, info:eu-repo/semantics/published

Les transformations de transformations, également appelées processus d'ordres supérieurs, forment un concept courant en informatique et en traitement de l'information. De tels processus apparaissent dès qu'il est question de manipulations sur l'opération à appliquer aux données, plutôt que sur les données elles-mêmes. Par exemple, lorsque l'on veut représenter un protocole informatique avec des boucles de rétroaction d'opérations, comme des boucles "for" imbriquées, ou lorsque l'on veut représenter un protocole de communication avec un contrôle dynamique des opérations, comme lorsqu'un adversaire agit sur les données d'entrée et de sortie d'une autre partie afin de la tromper, on utilisera des processus d'ordre supérieur.Ce paradigme appliqué à l'informatique quantique a récemment suscité un grand intérêt, tant au niveau pratique que fondamental. D'une part, il a été démontré que certains processus quantiques d'ordre supérieur permettaient de réduire le nombre d'opérations nécessaires à la réalisation de certains protocoles. D'autre part, ces processus présentent parfois des relations causales indéfinies au sens quantique du terme ;l'ordre des événements A et B peut se superposer entre A puis B et B puis A. Ce comportement est d'un grand intérêt fondamental car il remet en question certaines idées préconçues que d'aucun pensent incompatibles avec une théorie quantique de la gravité.Un cadre général pour représenter les transformations quantiques d'ordres supérieurs est dès lors nécessaire pour pleinement exploiter les améliorations qu'elles apportent et, en parallèle, pour étudier les relations causales quantiques singulières qu'elles présentent. Pareil cadre est développé dans cette thèse. Plus précisément, un ensemble d'outils pour caractériser les processus quantiques d'ordre supérieurs valides reposant sur la dualité canal-état ainsi que l'utilisation de projecteurs superopératoires est présenté. Il est montré que les manières possibles de définir un ensemble do, Transformations of transformations, also called higher-order processes, is a commonly occurring concept in computing and information processing. Such processes arise in situations involving manipulations of the operation applied to the data, rather than of the data itself. For example, when one wants to represent a computing protocol with feedback loops of operations, like nested 'for loops', or when one wants to represent a communication protocol with dynamical control over operations, like where an adversary party is acting on the input and output data of some other party so to deceive her, higher-order processes will be used. Applied to quantum computing, this paradigm has recently attracted significant interest both at the practical and fundamental levels. On the one hand, specific higher-order quantum processes were shown to decrease the number of operations needed to realize certain protocols. On the other hand, these processes sometimes feature causal relations that are ‘indefinite’ in the quantum sense; the ordering of events A and B can become superposed between A then B and B then A. This behavior is of great fundamental interest as it challenges some pre-conceived ideas some believe to be incompatible with a quantum theory of gravity. A general framework to represent higher-order quantum transformations is then necessary to fully harness the improvements they provide and, in parallel, to study the puzzling quantum causal relations they feature. Such a framework is developed in this thesis. Specifically, a set of tools for characterizing valid higher-order quantum processes relying on channel-state duality and the use of superoperator projectors is presented. It is shown that the possible ways to define a given set of higher-order transformations are homomorphic to an algebra of these superoperator projectors, which are in turn homomorphic to the signaling relations that the objects in this set may allow. Moreover, this algebra is shown to be very close to, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

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This thesis investigates multiphoton quantum interference with a particular emphasis onphotonic partial distinguishability stemming from factors such as timelags or polarizationmismatches between the photons. We explore the gray area between the behaviour ofdistinguishable classical particles and ideally indistinguishable bosons in large linearinterferometers, with practical implications for photonic quantum computers – especiallyboson samplers – as well as fundamental consequences on the many-body physics ofbosonic systems.Our research leverages recent findings in the mathematical theory of matrix perma-nents to unravel new aspects of interference phenomena. In particular, we exhibit asurprising counterexample to the rule of thumb that "identical bosons bunch most",which can be observed with 7 photons in a 7-mode linear interferometer.We develop robust techniques to validate boson samplers – that is, to verify theincompatibility with classical samplers – by analyzing the photon distribution amongpartitions of the output modes. This innovative method extends existing validationtests, providing a comprehensive approach to assessing boson sampling experiments.An extra contribution of this thesis is the development of BosonSampling.jl, anopen-source, high-performance software package for multiphoton interferometry simula-tions, featuring versatile tools for boson sampling tasks and a suite of validation tools inorder to rigorously evaluate boson samplers in the presence of partial distinguishabilityand other noise sources., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Experimental demonstrations of entangled quantum images produced through parametric down conversion have so far been confined to studying two-photon correlations. Here we show that multiphoton correlations between quantum images are accessible experimentally and exhibit many new features including being sensitive to the phase of the biphoton wave function. As a concrete example, we consider a modification of existing quantum imaging experiments in which the charge-coupled device cameras are moved out of focus, provide detailed analytical predictions for the resulting four-photon interferences, and support these by numerical simulations. The proposed experiment can also be interpreted as entanglement swapping: Bob's photons are initially unentangled, but the joint detection of Alice's photons projects Bob's photons onto an entangled state. The general approach proposed here can be extended to other quantum optics experiments involving high-dimensional entanglement., SCOPUS: ar.j, info:eu-repo/semantics/published

La non-classicalité d'un état monomode de la lumière et l'intrication d'états photoniques bipartites sont des phénomènes quantiques centraux composant deux des différences les plus essentielles entre les domaines classique et quantique. Depuis leur découverte, ces propriétés ont suscité un intérêt considérable et constant de la part de la communauté des physiciens, dans le but de développer des protocoles basés sur ces phénomènes et qui n'ont pas d'équivalent classique. Pour prendre un seul exemple, l'intrication de deux photons peut être utilisée comme ressource pour effectuer de la cryptographie quantique, c'est-à-dire pour distribuer une clé secrète de manière sécurisée entre deux parties qui n'ont même pas besoin de faire confiance à leurs dispositifs quantiques. Afin d'exploiter ces propriétés et de développer des sources optiques d'états non-classiques ou intriqués, il est crucial de pouvoir détecter si l'état émis par la source est effectivement non-classique ou intriqué. Dans cette optique, de nombreux témoins (conditions suffisantes) de non-classicalité ou d'intrication ont été conçus au fil des années.Dans cette thèse, nous nous intéressons particulièrement à une hiérarchie de critères qui a été développée par Shchukin, Richter et Vogel au début des années 2000. Le témoin le plus courant de l'intrication est le critère PPT de "positive partial transpose", qui stipule que tout état séparable doit rester physique après avoir subi une transposition partielle. Si cette condition n'est pas remplie, cela signifie que l'état est intriqué. Sur cette base, un ensemble complet de critères a été exprimé par ces auteurs à partir d'une matrice de moments des opérateurs de mode (création et annihilation). De même, un ensemble de critères a été construit sur la base d'une matrice de moments dans l'ordre normal afin d'exprimer la non-négativité de la fonction P de Glauber, donnant lieu à une hiérarchie de témoins de non-classicalité.La principale difficulté dans la détect, The so-called nonclassicality of a single-mode state of light and the entanglement of bipartite photonic states are central quantum phenomena which underlie two of the most essential differences between the classical and the quantum. Since their discovery, these properties have attracted a tremendous, constant interest from the quantum physics community, with the goal of developing protocols that take advantage of them and have no classical counterpart. To take a single example, the entanglement of two photons can be used as a resource to perform quantum cryptography in a device-independent manner, that is, to distribute a secret key in a secure way between two parties who do not even need to trust their quantum devices. In order to exploit these properties and develop optical sources of nonclassical or entangled states, it is crucial to be able to detect whether the state emitted by the source is effectively nonclassical or entangled. Along this way, numerous witnesses (sufficient conditions) for nonclassicality or entanglement have been conceived over the years.In this thesis, we are especially interested in a hierarchy of criteria that has been developed by Shchukin, Richter, and Vogel in the early 2000s. The most common witness of entanglement is the PPT criterion for "positive partial transpose'', which states that any separable state must remain physical after undergoing a partial transpose. If this condition is not met, it means that the state is entangled. Based on this, a complete set of criteria was expressed by these authors based on a matrix of moments of the mode (creation and annihilation) operators. Similarly, a set of criteria was built based on a matrix of normally-ordered moments in order to express the non-negativity of the Glauber-Sudarshan P-function, giving rise to a hierarchy of nonclassicality witnesses.The main difficulty in the practical detection of nonclassicality or entanglement is the measurement of the quantities that are needed to app, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

Entanglement is a defining property of quantum theory and plays a central role in the phenomenon of non-locality, which is revealed by the violation of Bell inequalities. Importantly, this allows us to study and characterize quantum systems in a device-independent way, i.e. without making any assumptions about the devices used to generate and manipulate quantum states, but only from the observed correlations between measurement results. In addition to entanglement, another mechanism for establishing correlations between quantum systems is direct communication between them. Similar to the Bell scenario, one can study correlations generated by quantum communication in prepare-and-measure scenarios via a semi-device-independent approach, where certain minimal assumptions about the experimental setup are assumed. A third way to establish correlations between quantum systems is through the combined effect of entanglement and quantum communication. Although many quantum information protocols use these two mechanisms, little work has been done to characterize the resulting correlations.This thesis initiates the systematic study of entanglement-assisted prepare-and-measure correlations. We develop a suite of tools that enable us to characterize correlations in such scenarios and apply those tools to solve relevant problems in quantum information.We construct novel, entanglement-robust, device-independent dimension witnesses and derive new resource inequalities. We adapt our tools to re-examine entanglement advantages in distributed classical communication tasks and identify a class of protocols that outperform the conventional protocols predominant in the literature.We also examine the challenges involved in experimental implementations of entanglement-assisted quantum communication on photonic platforms. Our theoretical and experimental findings show how information-theoretically relevant tasks beyond the boosting of channel capacities can be accomplished using qubit commu, L'intrication est une propriété fondamentale des systèmes quantiques et joue un rôle central dans le phénomène de non-localité mis en évidence par la violation des inégalités de Bell. Elle permet notamment d'étudier et de caractériser les systèmes quantiques de manière `device-independent', c'est-à-dire sans faire d'hypothèses sur les appareils utilisés pour générer et manipuler des états quantiques, mais uniquement à partir des corrélations observées entre résultats de mesures. Outre l'intrication, un autre mécanisme pour établir des corrélations entre systèmes quantiques, est la communication directe entre eux. De manière analogue au scénario de Bell, il est possible d'étudier les corrélations générées par communication quantique dans les scénarios de type `prepare-and-measure' via une approche `semi-device-independent' où on suppose certaines hypothèses minimales sur le dispositif expérimental. Une troisième façon d'établir des corrélations entre systèmes quantiques est par l'effet combiné de l'intrication et de la communication quantique. Bien que de nombreux protocoles d'information quantique utilisent ces deux mécanismes, peu de travaux se sont intéressés à caractériser les corrélations qui en résultent.Nous initions dans cette thèse l'étude systématique des corrélations obtenues par l'effet conjoint de l'intrication et de la communication quantique dans des scenarios de type `prepare-and-measure'. Nous développons une série d'outils qui nous permettent de caractériser ces corrélations et utilisons ces outils pour résoudre des problèmes associés en informatique quantique.Nous construisons de nouveaux témoins de dimension `device-independent' robustes à l'intrication, et étudions les relations entre communication et intrications vues comme des ressources. Nous adaptons nos outils pour réexaminer les avantages de l'intrication en présence de communication classique et identifions une classe de protocoles qui surpassent les protocoles conventionnels prédominants, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a factor of 7/9. Extending the works cite{Hastings2017} and cite{Campbell2017}, we show that taking probabilistic mixtures of channels to solve fallback cite{BRS2015} and magnitude approximation problems saves factor of two in approximation costs. In particular, over the Clifford+ T gate set we achieve an average non-Clifford gate count of 0.23 log 2 &x2061; ( 1 / &x03B5; ) + 2.13 and T-count 0.56 log 2 &x2061; ( 1 / &x03B5; ) + 5.3 with mixed fallback approximations for diamond norm accuracy &, SCOPUS: ar.j, info:eu-repo/semantics/published

Applying time-periodic modulations is routinely used to control and design synthetic matter in quantum-engineered settings. In lattice systems, this approach is explored to engineer band structures with non-trivial topological properties, but also to generate exotic interaction processes. A prime example is density-assisted tunneling, by which the hopping amplitude of a particle between neighboring sites explicitly depends on their respective occupations. Here, we show how density-assisted tunneling can be tailored in view of simulating the effects of strain in synthetic graphene-type systems. Specifically, we consider a mixture of two atomic species on a honeycomb optical lattice: one species forms a Bose-Einstein condensate in an anisotropic harmonic trap, whose inhomogeneous density profile induces an effective uniaxial strain for the second species through density-assisted tunneling processes. In direct analogy with strained graphene, the second species experiences a pseudo-magnetic field, hence exhibiting relativistic Landau levels and the valley Hall effect. Our proposed scheme introduces a unique platform for the investigation of strain-induced gauge fields, opening the door to future studies of their possible interplay with quantum fluctuations and collective excitations., SCOPUS: ar.j, info:eu-repo/semantics/published

Dense coding is the seminal example of how entanglement can boost qubit communication, from sending one bit to sending two bits. This is made possible by projecting separate particles onto a maximally entangled basis. We investigate more general communication tasks, in both theory and experiment, and show that simpler measurements enable strong and sometimes even optimal entanglement-assisted qubit communication protocols. Using only partial Bell state analysers for two qubits, we demonstrate quantum correlations that cannot be simulated with two bits of classical communication. Then, we show that there exists an established and operationally meaningful task for which product measurements are sufficient for the strongest possible quantum predictions based on a maximally entangled two-qubit state. Our results reveal that there are scenarios in which the power of entanglement in enhancing quantum communication can be harvested in simple and scalable optical experiments., SCOPUS: ar.j, info:eu-repo/semantics/published

The propagation of a fast particle in a low-density gas at thermal equilibrium is studied in the context of quantum mechanics. A quantum master equation in the Redfield form governing the reduced density matrix of the particle is derived explicitly from first principles. Under some approximations, this equation reduces to the linear Boltzmann equation. The issue of the positivity of the time evolution is also discussed by means of a Lindblad form. The Born and Markov assumptions underlying these equations, as well as other approximations regarding the bath correlation function, are discussed in detail. Furthermore, all these master equations are shown to be equivalent with each other if the density matrix of the particle is diagonal in the momentum basis, or if the collision rate is independent of the particle momentum., SCOPUS: ar.j, info:eu-repo/semantics/published

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L’espace des phases est un outil mathématique essentiel pour l’étude des systèmes dynamiques en mécanique classique. Cet espace abstrait, dont les coordonnées sont les variables dynamiques d’un système, peut également être exploité pour la caractérisation des systèmes en physique quantique, et plus particulièrement en optique quantique. Cependant, alors que l’état d’une particule en mouvement en mécanique classique à un instant donné est représenté par un point dans l’espace des phases, l’état d’un système photonique en optique quantique est beaucoup plus complexe et doit être représenté par une distribution de quasi-probabilité, telle que la fonction de Wigner. Par rapport à une distribution ponctuelle, cette répartition rend compte de la nature quantique du système et trouve son origine dans le principe d’incertituded’Heisenberg. Une autre spécificité de l’espace des phases quantique qui n’a pas d’analogue classique réside dans le fait qu’une distribution de quasi-probabilité peut admettre des valeurs négatives ou même ne pas être exprimable comme une fonction régulière.La représentation de l’état du champ électromagnétique en optique quantique est généralement basée sur des distributions de quasi-probabilité dans l’espace des phases quantique. Ici, les variables dynamiques qui sont considérées sont les quadratures (x, p) du champ électromagnétique. Une telle représentation de l’espace des phases permet de visualiser l’état et constitue une alternative à une description en termes de matrice densité. Il est important de noter qu’il n’existe généralement pas d’équivalence simple entre les caractéristiques de la distribution de quasi-probabilité et les propriétés de l’état quantique correspondant. Par exemple, le fait que la fonction de Wigner admette des valeurs négatives est une condition suffisante (mais non nécessaire) pour la non-classicalité de l’état correspondant (c’est-à-dire son incompatibilité avec un mélange d’états cohérents). L’espace des phases quantiq, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

The main purpose of this thesis is to investigate the physics of particle detectors from first principles combining quantum mechanics and statistical physics. In particular, this work aims at studying the Mott problem, that is the issue of the appearance, within the framework of quantum mechanics, of linear tracks in Wilson cloud chambers due to the passage of ionizing particles. Although the Mott problem is closely related to the quantum measurement problem, this thesis focuses on the phenomenological questions regarding the propagation of a quantum particle in a detector rather than the question of the interpretation of quantum mechanics. To this end, models of a quantum particle evolving in a gaseous environment are developed. In the first considered model, called the random Lorentz gas, the constituents of the medium are assumed to be point-like and fixed at random positions. The Schrödinger equation can thus be solved systematically using the Foldy-Lax method. This model is first studied with the tools of scattering theory, namely the cross section and the complex resonance spectrum. An efficient numerical method is devised to compute the density of resonances in the complex plane of the wavenumber, without having to find them one by one. This method leads to hitherto unknown structures in the resonance spectrum. These structures are then explained by resorting to wave transport theory, which includes an effective Schrödinger equation at large wavelength, and an integral transport equation at small wavelength. The phase averaging effect is especially highlighted in the latter case. This effect is the cancellation of most of the off-diagonal elements of the density matrix after the average over the random configurations of the scatterers. The second considered model is more comprehensive, as it accounts for the quantum nature of the gaseous environment. The density matrix of the full system is governed by the quantum Liouville equation. Since the gas is in a the, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

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Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a quadratic advantage over classical random walks has been an outstanding problem. Thus far, this advantage is obtained only for specific graphs or when a single node of the underlying graph is marked. In this Letter, we provide a new continuous-time quantum walk search algorithm that completely resolves this: our algorithm can find a marked node in any graph with any number of marked nodes, in a time that is quadratically faster than classical random walks. The overall algorithm is quite simple, requiring time evolution of the quantum walk Hamiltonian followed by a projective measurement. A key component of our algorithm is a purely analogue procedure to perform operations on a state of the form e-tH2, SCOPUS: ar.j, info:eu-repo/semantics/published

A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point scatterers is derived in detail and expressed in terms of the scattering length. The fundamental properties of the model, such as the cross section and the scattering matrix, are calculated. In addition, the model is shown to verify the optical theorem and thus probability conservation. Finally, the differential and total cross sections are numerically computed in two situations whether the Lorentz gas is smaller or larger than the mean free path. A distinct Airy diffraction peak is obtained for a large enough number of scatterers. This observation is related to the extinction paradox., SCOPUS: ar.j, info:eu-repo/semantics/published

The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wave number without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a nonresonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer resonance are identified as proximity resonances. Moreover, the hard-sphere model is used to reveal previously unknown structures in the resonance density. Finally, it is shown how Anderson localization affects the distribution of resonance widths, especially in the one-dimensional case., SCOPUS: ar.j, info:eu-repo/semantics/published

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This thesis is centered on a novel approach to quantum uncertainty based on applying the theory of continuous majorization to quantum phase-space distributions. Majorization theory is a powerful mathematical framework that is aimed at comparing distributions with respect to intrinsic disorder. It is particularly significant in the sense that establishing a majorization relation between two distributions amounts to proving that every (Shur-concave) measure of disorder will categorize one distribution as more ordered than the other. Although this is less known, the distributions here do not need to be normalized nor positive for majorization theory to apply, so the latter even extends beyond probability distributions. Further, a majorization relation can rigorously be defined for both discrete and continuous distributions over a finite-size domain, as well as for (discrete and continuous) distributions that are positive over an infinite-size domain.The central thrust of this thesis is to characterize quantum uncertainty in phase space by applying the tools of majorization theory to the Wigner function, which is the most common (quasi)distribution that embodies a quantum state in phase space. Wigner functions are in general positive and negative, putting them beyond the reach of most information-theoretical measures but perfect candidates for the theory of majorization. We start our manuscript with a succinct overview of the basics of quantum optics in phase space, which are a prerequisite for the characterization of disorder in phase space. This gives us the occasion to present a secondary achievement of the thesis consisting in establishing a resource theory for local Gaussian work extraction, which exploits the symplectic formalism within quantum thermodynamics. In this context, work can be defined as the difference between the trace and symplectic trace of the covariance matrix of the state, and it displays a number of interesting properties. Back to our primary in, Cette thèse est centrée sur une nouvelle approche de l'incertitude quantique basée sur l'application de la théorie de la majorisation continue aux distributions de l'espace des phases quantique. La théorie de la majorisation est un cadre mathématique puissant qui vise à comparer des distributions par rapport à leur désordre intrinsèque. Elle est particulièrement importante dans le sens où établir une relation de majorisation entre deux distributions revient à prouver que toute mesure (Shur-concave) du désordre classera une distribution comme plus ordonnée que l'autre. Bien que cela soit moins connu, les distributions ici n'ont pas besoin d'être normalisées ni positives pour que la théorie de la majorisation s'applique, de sorte que cette dernière s'étend même au-delà des distributions de probabilité. De plus, une relation de majorisation peut être rigoureusement définie pour les distributions discrètes et continues sur un domaine de taille finie, ainsi que pour les distributions (discrètes et continues) qui sont positives sur un domaine de taille infinie. L'idée maîtresse de cette thèse est de caractériser l'incertitude quantique dans l'espace des phases en appliquant les outils de la théorie de la majorisation à la fonction de Wigner, qui est la (quasi-)distribution la plus commune qui incarne un état quantique dans l'espace des phases. Les fonctions de Wigner sont en général positives et négatives, ce qui les place hors de portée de la plupart des mesures de la théorie de l'information mais en fait des candidats parfaits pour la théorie de la majorisation. Nous commençons notre manuscrit par un aperçu succinct des bases de l'optique quantique dans l'espace de phase, qui sont une condition préalable à la caractérisation du désordre dans l'espace des phases. Cela nous donne l'occasion de présenter une réalisation secondaire de la thèse consistant à établir une théorie des ressources pour l'extraction du travail gaussien local, qui exploite le formalisme symplectique, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality of this sort is whether or not the predictions of a given operational theory can be explained by a generalized-noncontextual ontological model. We here explore what notion of classicality this implies for the generalized probabilistic theory (GPT) that arises from a given operational theory, focusing on prepare-measure scenarios. We first show that, when mapping an operational theory to a GPT by quotienting relative to operational equivalences, the constraint of explainability by a generalized-noncontextual ontological model is mapped to the constraint of explainability by an ontological model. We then show that, under the additional assumption that the ontic state space is of finite cardinality, this constraint on the GPT can be expressed as a geometric condition which we term simplex embeddability. Whereas the traditional notion of classicality for a GPT is that its state space be a simplex and its effect space be the dual of this simplex, simplex embeddability merely requires that its state space be embeddable in a simplex and its effect space in the dual of that simplex. We argue that simplex embeddability constitutes an intuitive and freestanding notion of classicality for GPTs. Our result also has applications to witnessing nonclassicality in prepare-measure experiments., SCOPUS: ar.j, info:eu-repo/semantics/published

We introduce a weak form of the realignment separability criterion which is particularly suited to detect continuous-variable entanglement and is physically implementable (it requires linear optics transformations and homodyne detection). Moreover, we define a family of states, called Schmidt-symmetric states, for which the weak realignment criterion reduces to the original formulation of the realignment criterion, making it even more valuable as it is easily computable especially in higher dimensions. Then, we focus in particular on Gaussian states and introduce a filtration procedure based on noiseless amplification or attenuation, which enhances the entanglement detection sensitivity. In some specific examples, it does even better than the original realignment criterion., SCOPUS: ar.j, info:eu-repo/semantics/published

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Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent., SCOPUS: ar.j, info:eu-repo/semantics/published

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Measurements in quantum theory exhibit incompatibility, i.e. they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint measurability structure: its vertices represent measurements and its hyperedges represent (all and only) subsets of compatible measurements. Projective measurements in quantum theory realize (all and only) joint measurability structures that are graphs. On the other hand, general measurements represented by positive operator-valued measures (POVMs) can realize arbitrary joint measurability structures. Here we explore the scope of joint measurability structures realizable with qubit POVMs. We develop a technique that we term marginal surgery to obtain nontrivial joint measurability structures starting from a set of compatible measurements. We show explicit examples of marginal surgery on a special set of qubit POVMs to construct joint measurability structures such as N-cycle and N-Specker scenarios for any integer N≥3. We also show the realizability of various joint measurability structures with N∈{4,5,6} vertices. In particular, we show that all possible joint measurability structures with N=4vertices are realizable. We conjecture that all joint measurability structures are realizable with qubit POVMs. This contrasts with the unbounded dimension required in R. Kunjwal et al. [Phys. Rev. A 89, 052126 (2014)]. Our results also render this previous construction maximally efficient in terms of the required Hilbert space dimension. We also obtain a sufficient condition for the joint measurability of any set of binary qubit POVMs which powers many of our results and should be of independent interest., 0, SCOPUS: ar.j, info:eu-repo/semantics/published

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular causal structure, namely, one wherein the wings are only connected by a common cause. We term them “common-cause boxes”. We define the distinction between classical and nonclassical resources in terms of whether or not a classical causal model can explain the correlations. One can then quantify the relative nonclassicality of resources by considering their interconvertibility relative to the set of operations that can be implemented using a classical common cause (which correspond to local operations and shared randomness). We prove that the set of free operations forms a polytope, which in turn allows us to derive an efficient algorithm for deciding whether one resource can be converted to another. We moreover define two distinct monotones with simple closed-form expressions in the two-party binary-setting binary-outcome scenario, and use these to reveal various properties of the pre-order of resources, including a lower bound on the cardinality of any complete set of monotones. In particular, we show that the information contained in the degrees of violation of facet-defining Bell inequalities is not sufficient for quantifying nonclassicality, even though it is sufficient for witnessing nonclassicality. Finally, we show that the continuous set of convexly extremal quantumly realizable correlations are all at the top of the pre-order of quantumly realizable correlations. In addition to providing new insights on Bell nonclassicality, our work also sets the stage for quantifying nonclassicality in more general causal networks., SCOPUS: re.j, info:eu-repo/semantics/published

One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)PLRAAN1050-294710.1103/PhysRevA.70.022314], finds a marked node on a graph of n nodes via a continuous-time quantum walk. This algorithm is said to be optimal if it can find any of the nodes in O(n) time. However, given a graph, no general conditions for the optimality of the algorithm are known and previous works demonstrating optimal quantum search for certain graphs required an instance-specific analysis. In fact, the demonstration of the necessary and sufficient conditions that a graph must fulfill for quantum search to be optimal has been a long-standing open problem. In this work we make significant progress towards solving this problem. We derive general expressions, depending on the spectral properties of the Hamiltonian driving the walk, that predict the performance of this quantum search algorithm provided certain spectral conditions are fulfilled. Our predictions are valid, for example, for (normalized) Hamiltonians whose spectral gap is considerably larger than n-1/2. This allows us to derive necessary and sufficient conditions for optimal quantum search in this regime, as well as provide examples of graphs where quantum search is suboptimal. In addition, by extending this analysis, we are also able to show the optimality of quantum search for certain graphs with very small spectral gaps, such as graphs that can be efficiently partitioned into clusters. Our results imply that, to the best of our knowledge, all prior results analytically demonstrating the optimality of this algorithm for specific graphs can be recovered from our general results., SCOPUS: ar.j, info:eu-repo/semantics/published

The fundamental problem of sampling from the limiting distribution of quantum walks on networks, known as mixing, finds widespread applications in several areas of quantum information and computation. Of particular interest in most of these applications is the minimum time beyond which the instantaneous probability distribution of the quantum walk remains close to this limiting distribution, known as the "quantum mixing time". However, this quantity is only known for a handful of specific networks. In this Letter, we prove an upper bound on the quantum mixing time for almost all networks, i.e. the fraction of networks for which our bound holds, goes to one in the asymptotic limit. To this end, using several results in random matrix theory, we find the quantum mixing time of Erdös-Renyi random networks: networks of n nodes where each edge exists with probability p independently. For example, for dense random networks, where p is a constant, we show that the quantum mixing time is O(n3/2+o(1)). In addition to opening avenues for the analytical study of quantum dynamics on random networks, our work could find applications beyond quantum information processing. Owing to the universality of Wigner random matrices, our results on the spectral properties of random graphs hold for general classes of random matrices that are ubiquitous in several areas of physics. In particular, our results could lead to novel insights into the equilibration times of isolated quantum systems defined by random Hamiltonians, a foundational problem in quantum statistical mechanics., SCOPUS: ar.j, info:eu-repo/semantics/published

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical mixing time. In this article, we deal with analog quantum algorithms for mixing. First, we provide an analog quantum algorithm that, given a Markov chain, allows us to sample from its stationary distribution in a time that scales as the sum of the square root of the classical mixing time and the square root of the classical hitting time. Our algorithm makes use of the framework of interpolated quantum walks and relies on Hamiltonian evolution in conjunction with von Neumann measurements. There also exists a different notion for quantum mixing: the problem of sampling from the limiting distribution of quantum walks, defined in a time-averaged sense. In this scenario, the quantum mixing time is defined as the time required to sample from a distribution that is close to this limiting distribution. Recently, we provided an upper bound on the quantum mixing time for Erdos-Rényi random graphs [Phys. Rev. Lett. 124, 050501 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.050501]. Here, we also extend and expand upon our findings therein. Namely, we provide an intuitive understanding of the state-of-the-art random matrix theory tools used to derive our results. In particular, for our analysis we require information about macroscopic, mesoscopic, and microscopic statistics of eigenvalues of random matrices which we highlight here. Furthermore, we provide numerical simulations that corroborate our analytical findings and extend this notion of mixing from simple graphs to any ergodic, reversible, Markov chain., SCOPUS: ar.j, info:eu-repo/semantics/published

Spatial search by a discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain P quadratically faster than its classical counterpart, i.e. in a time that is in the square root of the hitting time of P. However, in the framework of continuous-time quantum walks, it was previously unknown whether such general speedup is possible. In fact, in this framework, the widely used quantum algorithm by Childs and Goldstone fails to achieve such a speedup. Furthermore, it is not clear how to apply this algorithm for searching any Markov chain P. In this article we aim to reconcile the apparent differences between the running times of spatial search algorithms in these two frameworks. We first present a modified version of the Childs and Goldstone algorithm which can search for a marked element for any ergodic, reversible P by performing a quantum walk on its edges. Although this approach improves the algorithmic running time for several instances, it cannot provide a generic quadratic speedup for any P. Second, using the framework of interpolated Markov chains, we provide a spatial search algorithm by a continuous-time quantum walk which can find a marked node on any P in the square root of the classical hitting time. In the scenario where multiple nodes are marked, the algorithmic running time scales as the square root of a quantity known as the extended hitting time. Our results establish a connection between discrete-time and continuous-time quantum walks and can be used to develop a number of Markov chain-based quantum algorithms., SCOPUS: ar.j, info:eu-repo/semantics/published

Contextuality is one way of capturing the nonclassicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of noncontextuality inequalities-certain linear inequalities involving probabilities of measurement events. Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [Cabello Phys. Rev. A 88, 032104 (2013)10.1103/PhysRevA.88.032104; Chudnovsky Ann. Math. 164, 51 (2006)10.4007/annals.2006.164.51] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anticyclically exclusive. Thus, the noncontextuality inequalities the underlying exclusivity structure of which is as stated, either cyclic or anticyclic, are fundamental to quantum theory. We show that there is a unique noncontextuality inequality for each nontrivial cycle and anticycle. In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing., SCOPUS: ar.j, info:eu-repo/semantics/published

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In the context of multiparameter quantum estimation theory, we investigate the construction of linear schemes in order to infer two classical parameters that are encoded in the quadratures of two quantum coherent states. The optimality of the scheme built on two phase-conjugate coherent states is proven with the saturation of the quantum Cramér–Rao bound under some global energy constraint. In a more general setting, we consider and analyze a variety of n-mode schemes that can be used to encode n classical parameters into n quantum coherent states and then estimate all parameters optimally and simultaneously., SCOPUS: ar.j, info:eu-repo/semantics/published

The evolution of a quantum particle in a gaseous detector governed by the Schrödinger equation is studied by means of a simplified 3D model. The particle is assumed to interact with N excitable two-level point-like scatterers depicting the atoms. In this model, the energy loss experienced by the particle after atomic excitations is accounted for. Using the Green function method, the full wave function is uniquely determined by N times 2 to the power N complex numbers. Remarkably, the Lippmann-Schwinger equation of this multi-scattering problem can be exactly solved in a non-perturbative way. The aim is to analyze the influence of the initial microstate of the detector on the observed outcome, and to understand the mechanism of track formation in gaseous detectors., info:eu-repo/semantics/published

The mathematical relations between the regular Coulomb function Fηℓ(ρ) and the irregular Coulomb functions H±ηℓ(ρ) and Gηℓ(ρ) are obtained in the complex plane of the variables η and ρ for integer or half-integer values of ℓ. These relations, referred to as “connection formulas,” form the basis of the theory of Coulomb wave functions and play an important role in many fields of physics, especially in the quantum theory of charged particle scattering. As a first step, the symmetry properties of the regular function Fηℓ(ρ) are studied, in particular, under the transformation ℓ ↦ −ℓ − 1, by means of the modified Coulomb function Φηℓ(ρ), which is entire in the dimensionless energy η−2 and the angular momentum ℓ. Then, it is shown that, for integer or half-integer ℓ, the irregular functions H±ηℓ(ρ) and Gηℓ(ρ) can be expressed in terms of the derivatives of Φη,ℓ(ρ) and Φη,−ℓ−1(ρ) with respect to ℓ. As a consequence, the connection formulas directly lead to the description of the singular structures of H±ηℓ(ρ)and Gηℓ(ρ) at complex energies in their whole Riemann surface. The analysis of the functions is supplemented by novel graphical representations in the complex plane of η−1., SCOPUS: ar.j, info:eu-repo/semantics/published