La théorie du calcul quantique se situe à la frontière de la physique quantique et de l’informatique. Par conséquent, les deux domaines contribuent à la rendre d’autant plus riche en apportant leurs propres méthodes et outils mathématiques. La présente thèse tente de mettre en évidence cette particularité en traitant des problématiques qui vont la physique expérimentale aux modèles de calcul. Le but est d’offrir de nouvelles possibilités pour démontrer un avantage quantique. Après une brève introduction aux notions de base de la mécanique quantique, certains aspects liés à l’informatique sont discutés. Le formalisme des classes de complexité quantiques ainsi que le concept du calcul quantique en variables continues sont décrits. Ensuite, le modèle connu comme instantaneous quantum computing est traduit en variables continues, le rendant attrayant d’un point de vue expérimental. Le chapitre conclut sur une discussion concernant un protocole hybride impliquant l’algorithme de Grover dans le cadre des communications quantiques. La dernière partie de la thèse s’intéresse à des problématiques issues de la physique expérimentale. Le lien entre l’effet Hong-Ou-Mandel et la fonction de Wigner d’un état à deux photons est mise en évidence, et un protocole expérimental est décrit en conséquence. La suite traite du domaine des circuits supraconducteurs et envisage de possibles expériences. Il est montré comment utiliser un qubit de flux pour manipuler un centre coloré du diamant. Il est également décrit comment sonder le modèle de Rabi dans le régime de couplage ultra fort en utilisant un qubit supplémentaire faiblement couplé. / The theory of quantum computing lies at the very boundary between quantum physics and computer science. As such, both fields bring their own methods and mathematical tools to make quantum computing even richer. The present thesis attempts to reflect this specificity by addressing questions ranging from experimental physics to computational models. The goal is to provide novel ways of demonstrating quantum advantage. After a short introduction to basic notions of quantum mechanics, some computer science aspects are discussed. We describe the powerful formalism of quantum complexity classes and the concept of quantum computations based on continuous variables. We then translate the model of instantaneous quantum computing to continuous variables, which is experimentally appealing. The chapter concludes with a discussion on a hybrid protocol involving Grover’s algorithm in a quantum communication framework. The last part of the thesis is devoted to experimentally driven issues. A fundamental connection between the Hong-Ou-Mandel experiment and the Wigner function of two-photon states is derived and a verification protocol is designed accordingly. We then move to the field of superconducting circuits to discuss proposals for future experiments. We show how to use a flux qubit to manipulate a NV color center. We also describe how to use to probe the Rabi model in the ultra strong coupling regime using an additional weakly coupled qubit.

Investigamos as propriedades quânticas dos feixes de luz produzidos pelo oscilador paramétrico ótico (OPO) acima do limiar, tanto experimental quanto teoricamente. Apresentamos a primeira medida de emaranhamento entre os feixes gêmeos, sinal e complementar. Estes podem possuir frequências óticas muito distintas, correspondentes a centenas de nanometros em comprimento de onda. O emaranhamento entre duas cores possibilita transferir informação quântica entre diferentes regiões do espectro eletromagnético. A demonstração experimental do emaranhamento foi realizada mostrando que a soma de variâncias de observáveis tipo EPR dos campos, a subtração de intensidades e a soma das fases dos feixes, viola uma desigualdade que deve ser necessariamente satisfeita por todos os estados separáveis. Mostramos a presença de squeezing em ambos os observáveis, com os respectivos valores $\\Delta^2 p_- = 0,49(1)$ e $\\Delta^2 q_+ = 0,65(1)$ relativos ao ruído quântico padrão. A desigualdade violada resultou $\\Delta^2 p_- +\\Delta^2 q_+ = 1,14(2)< 2$. Isso solucionou um problema aberto desde 1988, quando se previu teoricamente pela primeira vez a existência desse emaranhamento. Mostramos teoricamente que as correlações quânticas se estendem ao feixe de bombeio refletido pelo OPO, culminando no emaranhamento entre os três feixes envolvidos no processo paramétrico. Tem-se, assim, a geração direta de emaranhamento tripartite entre três regiões muito distintas do espectro. O emaranhamento multicolor amplia ainda mais as possibilidades de conversão da cor da informação quântica, com aplicações em redes quânticas. As diversas melhorias que realizamos em nosso sistema durante a busca pelo emaranhamento bipartite trouxeram uma compreensão mais profunda sobre a física de seu funcionamento, além de tornar nosso OPO uma fonte estável de feixes de luz coerente emaranhados. Este trabalho vem incluir o OPO acima do limiar no ferramental da área de informação quântica com variáveis contínuas. Esperamos em breve aplicações muito interessantes desse sistema. / We investigate the quantum properties of the light beams produced by an optical parametric oscillator (OPO) above threshold, both experimentally and theoretically. We present the first measurement of entanglement between the bright twin beams, signal and idler. These may differ in wavelength by hundreds of nanometers, showing different \'colors\'. This special characteristic allows for the transfer of quantum information between different regions of the electromagnetic spectrum. Entanglement was experimentally demonstrated by showing that the sum of variances of two EPR-like observables, the subtraction of the beams intensities and the sum of their phases, violates an inequality necessarily fulfilled by all separable states. We obtained squeezing in both observables, with the respective values $\\Delta^2 p_- = 0,49(1)$ and $\\Delta^2 q_+ = 0,65(1)$ relative to the shot noise level. The violated inequality resulted $\\Delta^2 p_- + \\Delta^2 q_+ = 1,14(2)< 2$. This solved an old problem, enunciated in 1988, when this effect was theoretically predicted for the first time. We show theoretically that the quantum correlations extend to the pump beam reflected by the OPO as well, culminating in entanglement among the three fields involved in the parametric process. Therefore, the OPO actually produces tripartite entanglement among very distant spectral regions in a direct manner. Multicolor entanglement opens new possibilities in the frequency conversion of quantum information. The improvements we performed in our system in order to achieve this result have brought a deeper understanding of the phenomena involved, as well as a more stable system operation, resulting in the development of a reliable source of bright entangled light beams. This work has finally added the above-threshold OPO to the optical quantum information toolbox. We expect new and exciting applications to come in the near future.

The idea to assimilate classical information theory with quantum mechanics resulted in the creation of a new field in physics known as quantum information. One of the first papers in this new field occurred in the early 1970's when Stephen Wiesner wrote the seminal manuscript titled: "Conjugate Coding". However, its importance wasn't imme- diately recognized and wasn't published until 1983. The 1980's and 1990's saw a number of important papers published in quantum information leading to the subfields of quantum cryptography, quantum teleportation, quantum entanglement, distinguishability of quantum states, and quantum cloning. It was also during the 1980's, that a new model of computing, known as quantum computation, was beginning to emerge. It offered the possibility of solving certain problems faster than a classical computer by exploiting various properties of quantum mechanics. Research in this field was undoubtedly stimulated by a well known talk given by Richard Feynman in 1981 at MIT on quantum simulations. Both quantum information and quantum computation were initially developed with quantum discrete variables in mind. However, over the course of the last decade, there has been a significant increase in using quantum continuous variables. This thesis will focus on the topic of quantum information and quantum computation using continuous variables. Specifically, we will theoretically consider the cloning of continuous-variable entanglement, the distinguishability of Gaussian states, new continuous-variable quantum cryptography protocols and finally, the universality of quantum computation using continuous-variable cluster states.

The idea to assimilate classical information theory with quantum mechanics resulted in the creation of a new field in physics known as quantum information. One of the first papers in this new field occurred in the early 1970's when Stephen Wiesner wrote the seminal manuscript titled: "Conjugate Coding". However, its importance wasn't imme- diately recognized and wasn't published until 1983. The 1980's and 1990's saw a number of important papers published in quantum information leading to the subfields of quantum cryptography, quantum teleportation, quantum entanglement, distinguishability of quantum states, and quantum cloning. It was also during the 1980's, that a new model of computing, known as quantum computation, was beginning to emerge. It offered the possibility of solving certain problems faster than a classical computer by exploiting various properties of quantum mechanics. Research in this field was undoubtedly stimulated by a well known talk given by Richard Feynman in 1981 at MIT on quantum simulations. Both quantum information and quantum computation were initially developed with quantum discrete variables in mind. However, over the course of the last decade, there has been a significant increase in using quantum continuous variables. This thesis will focus on the topic of quantum information and quantum computation using continuous variables. Specifically, we will theoretically consider the cloning of continuous-variable entanglement, the distinguishability of Gaussian states, new continuous-variable quantum cryptography protocols and finally, the universality of quantum computation using continuous-variable cluster states.

Investigamos as propriedades quânticas dos feixes de luz produzidos pelo oscilador paramétrico ótico (OPO) acima do limiar, tanto experimental quanto teoricamente. Apresentamos a primeira medida de emaranhamento entre os feixes gêmeos, sinal e complementar. Estes podem possuir frequências óticas muito distintas, correspondentes a centenas de nanometros em comprimento de onda. O emaranhamento entre duas cores possibilita transferir informação quântica entre diferentes regiões do espectro eletromagnético. A demonstração experimental do emaranhamento foi realizada mostrando que a soma de variâncias de observáveis tipo EPR dos campos, a subtração de intensidades e a soma das fases dos feixes, viola uma desigualdade que deve ser necessariamente satisfeita por todos os estados separáveis. Mostramos a presença de squeezing em ambos os observáveis, com os respectivos valores $\\Delta^2 p_- = 0,49(1)$ e $\\Delta^2 q_+ = 0,65(1)$ relativos ao ruído quântico padrão. A desigualdade violada resultou $\\Delta^2 p_- +\\Delta^2 q_+ = 1,14(2)< 2$. Isso solucionou um problema aberto desde 1988, quando se previu teoricamente pela primeira vez a existência desse emaranhamento. Mostramos teoricamente que as correlações quânticas se estendem ao feixe de bombeio refletido pelo OPO, culminando no emaranhamento entre os três feixes envolvidos no processo paramétrico. Tem-se, assim, a geração direta de emaranhamento tripartite entre três regiões muito distintas do espectro. O emaranhamento multicolor amplia ainda mais as possibilidades de conversão da cor da informação quântica, com aplicações em redes quânticas. As diversas melhorias que realizamos em nosso sistema durante a busca pelo emaranhamento bipartite trouxeram uma compreensão mais profunda sobre a física de seu funcionamento, além de tornar nosso OPO uma fonte estável de feixes de luz coerente emaranhados. Este trabalho vem incluir o OPO acima do limiar no ferramental da área de informação quântica com variáveis contínuas. Esperamos em breve aplicações muito interessantes desse sistema. / We investigate the quantum properties of the light beams produced by an optical parametric oscillator (OPO) above threshold, both experimentally and theoretically. We present the first measurement of entanglement between the bright twin beams, signal and idler. These may differ in wavelength by hundreds of nanometers, showing different \'colors\'. This special characteristic allows for the transfer of quantum information between different regions of the electromagnetic spectrum. Entanglement was experimentally demonstrated by showing that the sum of variances of two EPR-like observables, the subtraction of the beams intensities and the sum of their phases, violates an inequality necessarily fulfilled by all separable states. We obtained squeezing in both observables, with the respective values $\\Delta^2 p_- = 0,49(1)$ and $\\Delta^2 q_+ = 0,65(1)$ relative to the shot noise level. The violated inequality resulted $\\Delta^2 p_- + \\Delta^2 q_+ = 1,14(2)< 2$. This solved an old problem, enunciated in 1988, when this effect was theoretically predicted for the first time. We show theoretically that the quantum correlations extend to the pump beam reflected by the OPO as well, culminating in entanglement among the three fields involved in the parametric process. Therefore, the OPO actually produces tripartite entanglement among very distant spectral regions in a direct manner. Multicolor entanglement opens new possibilities in the frequency conversion of quantum information. The improvements we performed in our system in order to achieve this result have brought a deeper understanding of the phenomena involved, as well as a more stable system operation, resulting in the development of a reliable source of bright entangled light beams. This work has finally added the above-threshold OPO to the optical quantum information toolbox. We expect new and exciting applications to come in the near future.

L’information quantique peut être traitée sur différents types de systèmes physiques. Elle peut également être traitée selon deux façons fondamentalement différentes, en usant soit des variables discrètes, soit des variables continues. Dans cette thèse, nous nous concentrons sur l’optique quantique en variables continues et les expériences étudiées sont basées sur l’utilisation de photons. Après une introduction à quelques notions de base de la mécanique quantique, nous présentons un protocole sous-universel d’informatique quantique, appelé Boson Sampling, précédé d’une partie exposant des éléments de théorie de la complexité nécessaires pour comprendre la preuve de supériorité quantique de ce protocole. Puis, nous proposons un modèle pour décrire la création de qudits intriqués dans une expérience réalisée au sein de notre équipe. Enfin, la dernière partie de cette thèse présente une interprétation physique plus fondamentale des résultats obtenus lors d’expériences de type Hong-Ou-Mandel avec des filtres en fréquence devant les photodétecteurs, et montre qu’il s’agit d’une partie d’un état chat de Schrödinger produit par post-sélection. / Quantum information can be processed on differents types of physical systems. It can also be processed in two fundamentally different ways, using either discrete or continuous variable implementations. In this thesis, we concentrate on quantum optics in continuous variables and the studied experiments are based on the use of photons. After an introduction to some basic notions of quantum mechanics, we present a subuniversal protocol of quantum computing, named Boson Sampling, preceded by a part exposing elements of complexity theory which are necessary to understand the quantum superiority proof of this protocol. Then, we propose a model to describe the creation of entangled qudits in an experiment done in the team. Finally, the last part of this thesis presents a more fundamental physical interpretation of the results obtained during Hong-Ou-Mandel experiments with frequency filters in front of the photodetectors, and shows that we have a part of a Schrödinger cat state, produced by postselection.

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L’information quantique peut être traitée de deux manières fondamentalement différentes: à l’aide de variables discrètes ou continues. Dans cette thèse, nous étudions de manière théorique la réalisation de protocoles d’information quantique dans les systèmes caractérisés par des variables continues. Pour ce faire, nous utilisons les variables modulaires comme outil afin de révéler des structures discrètes dans les états, opérations et observables. Le présent travail est fortement motivé par l’applicabilité expérimentale de nos idées dans des expériences d’optique quantique. Le thème principal de cette thèse est la formulation d’un cadre pour le traitement quantique de l’information dans l’espace des phases grâce aux variables modulaires. L’usage des variables modulaires permet d’encoder des états logique dans des espaces de Hilbert de dimension infinie et de définir des opérations qui permettent de les manipuler. En particulier, nous considérons des protocoles qui impliquent des mesures de variables modulaires qui permettent la lecture d’information discrète codée dans des variables continues. Grâce à ce formalisme, nous montrons comment il est possible de réaliser des tests des propriétés fondamentales de la mécanique quantique comme l’intrication, la non-localité ou la contextualité dans des espaces de Hilbert de dimensions finie ou infinie. Ensuite, nous discutons pourquoi les degrés de liberté transverse des photons sont des candidats naturels pour l’implémentation expérimentale des variables modulaires. À cet effet, nous démontrons comment il est possible d’utiliser l’effet Talbot - un effet d’interférence de champ proche - afin d’encoder de l’information discrète dans la distribution spatiales des photons. Finalement, nous montrons pour la première fois comment produire des photons intriqués de dimension arbitraire de manière déterministe en utilisant la conversion paramétrique et des éléments d’optique linéaire. / Quantum information can be processed in two fundamentally different ways, using either discrete- or continuous-variable implementations. In this thesis we study theoretically how to implement discrete quantum information protocols in physical objects characterized by continuous variables. In order to do so we use modular variables as a helpful tool to reveal discrete structures in continuous-variable states, operations and observables. The present work is strongly guided by the experimental applicability of our ideas in quantum optics experiments, with a particular focus on the transverse degrees of freedom of single photons. One of the main themes of this thesis is the formulation of a framework for quantum information processing in phase-space based on the use of modular variables. The latter permit us to introduce logical states and operations allowing to manipulate discrete quantum information encoded in infinite dimensional Hilbert spaces. In particular, we consider protocols that involve measurements of judiciously chosen logical observables enabling the readout of the encoded discrete quantum information. Based on this framework we show how to perform tests of fundamental properties of quantum mechanics, such as entanglement, Bell nonlocality and contextuality, in Hilbert spaces of various dimensions. Further on, we discuss the transverse degrees of freedom of single photons as a natural platform to manipulate and measure modular variables. In particular, we demonstrate how to process discrete quantum information encoded in the spatial distribution of single photons via the optical Talbot effect - a near-field interference effect. Finally, we show for the first time how to produce deterministically d-dimensional entangled photon pairs using spontaneous parametric down-conversion and linear optical elements only.

La mécanique quantique présente des propriétés étonnantes qui n'ont pas d'équivalent en physique classique. Ces propriétés sont au cœur des applications possibles de la mécanique quantique. Le thème principal de cette thèse est l'étude de deux des propriétés fondamentales de la mécanique quantique: la non-localité et la contextualité. Dans ce cadre, nous poursuivrons deux objectifs: premièrement, nous étudierons comment certains résultats obtenus pour les systèmes discrets peuvent être étendus aux systèmes décrits par des variables continues; deuxièmement nous étudierons comment il est possible de tester ces deux propriétés dans les systèmes quantiques décrits par des variables continues.Dans une première partie, nous étudions l'ensemble des distributions de probabilités locales et ``no-signaling'', c'est à dire qui ne permettent pas de transmettre d'information. Nous commençons par traduire le problème en terme de contraintes sur des espaces de mesures de probabilité. Nous introduisons ensuite un ensemble de mesures de probabilité qui sont les analogues en variables continues des probabilités découvertes par Popescu et Rohrlich dans le cas discret. Enfin, nous caractérisons l'ensemble des mesures de probabilité ``no-signaling''. Plus précisément, nous montrons que les mesures introduites sont des points extrémaux de l'ensemble des mesures de probabilité ``no-signaling'' et que leur enveloppe convexe est dense dans l'ensemble des mesures de probabilité ``no-signaling''. Dans une seconde partie nous nous intéressons à une preuve de la contextualité de la mécanique quantique dans une formulation qui ne dépend pas de l'état. Plus particulièrement, concernant l'inégalité de non-contextualité de Peres-Mermin, nous montrons qu'il est possible de la généraliser pour des observables définies sur des espaces de Hilbert de dimension arbitraire, voire infinie. Cette généralisation nous permet d'identifier les propriétés communes des observables qui conduisent à une violation maximale de l'inégalité de Peres-Mermin.En dernier lieu, nous nous intéressons à des états intriqués du champ électromagnétique de deux cavités. Ces états sont non-locaux et violent une inégalité de Bell formée de mesures de la parité déplacée. Nous étudions comment ces états peuvent être préparés et mesurés expérimentalement. Enfin, nous analysons l'effet des imperfections expérimentales et des pertes / Quantum mechanics has many intriguing properties that have no-classical analogs. These properties are at the heart of many quantum information protocols which offer the possibility to outperform their classical counterparts. This thesis is devoted to an investigation of two of the fundamental properties of quantum mechanics: non-locality and contextuality. The goal of this thesis is twofold. Firstly we will study how known results for discrete systems can be extended to continuous variables systems. Secondly, we will investigate how these properties can be tested in quantum systems characterized by continuous variables.Our work starts with an investigation of the set of local and no-signaling probability distributions. We develop a formalism for generic no-signaling black-box measurement devices with continuous outputs in terms of probability measures. We introduce the continuous-variable version of the famous Popescu-Rohrlich boxes and show that they violate the Tsirelson bound of an adequate continuous-variable Bell inequality. Finally, we perform a characterization of the geometry of the set of continuous-variable no-signaling correlations. More precisely, we show that the convex hull of those boxes is dense in the no-signaling set.We then study the contextuality of Quantum Mechanics in a state independent formulation. In particular, we study the Peres-Mermin state independent non-contextuality inequality, and show how it is possible to generalize the Peres-Mermin inequality to scenarios involving observables with an arbitrary number of outcomes. Specifically, we identify general conditions on the spectral decomposition of observables demonstrating state independent contextuality of quantum mechanics in this scenario.Lastly, we explore the non-local properties of entangled cat states, made of superpositions of coherent states stored in two spatially separated cavities. We show that even when taking into account the experimental imperfections such as the losses, a violation of local-realism is still possible, in the form of a violation of an appropriate Bell inequality

Quantum annealing is expected to be a powerful generic algorithm for solving hard combinatorial optimization problems faster than classical computers. Finding the solution to a combinatorial optimization problem is equivalent to finding the ground state of an Ising Hamiltonian. In today's quantum annealers the spins of the Ising Hamiltonian are mapped to superconducting qubits. On the other hand, dissipation processes degrade the success probability of finding the solution. In this thesis we set out to explore a newly proposed architecture for a noise-resilient quantum annealer that instead maps the Ising spins to continuous variable quantum states of light encoded in the field quadratures of a two-photon pumped Kerr- nonlinear resonator based on the proposal by Puri et al. (2017). In this thesis we study the Wigner negativity for this newly proposed architecture and evaluate its performance based on the negativity of the Wigner function. We do this by determining an experimental value to when the presence of losses become too detrimental, such that the Wigner function of the quantum state during the evolution within the anneal becomes positive for all times. Furthermore, we also demonstrate the capabilities of this continuous variable quantum annealer by simulating and finding the best solution of a small instance of the NP-complete subset sum problem and of the number partitioning problem.