It has been recognized for some years that the use of computer graphics systems has great potential for improving man/computer communication. In the past, however, the high cost of graphics hardware, and the lack of accepted principles for graphics programming, prevented the widespread use of such systems. Recently, hardware has become more readily available, and efforts have been made to develop graphics software standards. This report presents an overview of one of the proposed standards, the Core System, and also discusses a portable subroutine library, based on the the Core System, that has been developed for use at McMaster University. This library, called SSOCS, is written in Pascal, and allows a user to produce two-dimensional images without regard to the characteristics of the graphics devices being used. / Thesis / Master of Science (MS)

Quantum key distribution (QKD) allows two remote parties to generate secret keys for cryptographic purposes. Its security has been proven with some assumptions. However, practical realizations may not comply with all the assumptions, leading to various attacks. Founded on the observation that almost all attacks are on the detection part, measurement-device-independent QKD (MDI-QKD) was proposed to remove all such attacks. This thesis presents an implementation of the protocol. In our implementation, key bit information was encoded in the polarization states of weak coherent pulses at 1542 nm wavelength in optical fibers, and decoy state techniques were employed. We ensured stable polarization preparation and alignment and developed a QKD system over 10 km of standard Telecom fibers at 500 KHz repetition rate. Our work demonstrates the practicality of MDI-QKD protocol of removing all attacks, existing and yet to be discovered, on the detection part of a QKD system.

Quantum key distribution (QKD) allows two remote parties to generate secret keys for cryptographic purposes. Its security has been proven with some assumptions. However, practical realizations may not comply with all the assumptions, leading to various attacks. Founded on the observation that almost all attacks are on the detection part, measurement-device-independent QKD (MDI-QKD) was proposed to remove all such attacks. This thesis presents an implementation of the protocol. In our implementation, key bit information was encoded in the polarization states of weak coherent pulses at 1542 nm wavelength in optical fibers, and decoy state techniques were employed. We ensured stable polarization preparation and alignment and developed a QKD system over 10 km of standard Telecom fibers at 500 KHz repetition rate. Our work demonstrates the practicality of MDI-QKD protocol of removing all attacks, existing and yet to be discovered, on the detection part of a QKD system.

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 measurement data into a single quantity---the violation of a unique Bell inequality---, our method exploits a complete, multidimensional description of the black-box correlations that allows it to certify more randomness from the same number of measurements. We illustrate our results on a numerical simulation of the protocol using partially entangled states. / 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 (intrication ou communication quantique) par rapport aux méthodes de DIRNG existantes.Nous présentons par ailleurs une méthode de génération d'aléa basée sur une estimation statistique originale des corrélations des boîtes noires. Contrairement aux méthodes de DIRNG existantes, qui résument l'ensemble des mesures observées à une seule grandeur (la violation d'une inégalité de Bell unique), notre méthode exploite une description complète (et donc multidimensionnelle) des corrélations des boîtes noires qui lui permet de certifier une plus grande quantité d'aléa pour un même nombre de mesures. Nous illustrons ensuite cette méthode numériquement sur un système de qubits partiellement intriqués. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Since their original introduction, strongly complementary observables have been a fundamental ingredient of the ZX calculus, one of the most successful fragments of Categorical Quantum Mechanics (CQM). In this thesis, we show that strong complementarity plays a vastly greater role in quantum theory. Firstly, we use strong complementarity to introduce dynamics and symmetries within the framework of CQM, which we also extend to infinite-dimensional separable Hilbert spaces: these were long-missing features, which open the way to a wealth of new applications. The coherent treatment presented in this work also provides a variety of novel insights into the dynamics and symmetries of quantum systems: examples include the extremely simple characterisation of symmetry-observable duality, the connection of strong complementarity with the Weyl Canonical Commutation Relations, the generalisations of Feynman's clock construction, the existence of time observables and the emergence of quantum clocks. Secondly, we show that strong complementarity is a key resource for quantum algorithms and protocols. We provide the first fully diagrammatic, theory-independent proof of correctness for the quantum algorithm solving the Hidden Subgroup Problem, and show that strong complementarity is the feature providing the quantum advantage. In quantum foundations, we use strong complementarity to derive the exact conditions relating non-locality to the structure of phase groups, within the context of Mermin-type non-locality arguments. Our non-locality results find further application to quantum cryptography, where we use them to define a quantum-classical secret sharing scheme with provable device-independent security guarantees. All in all, we argue that strong complementarity is a truly powerful and versatile building block for quantum theory and its applications, and one that should draw a lot more attention in the future.

Quantum key distribution (QKD) protocols are intended to allow cryptographic keys to be generated and distributed in way that is provably secure based on inherent limitations, such as the no-cloning principle, imposed by quantum mechanics. This unique advantage compared with classical cryptography comes with an added difficulty: key bits in QKD protocols are encoded in analogue quantum states and their preparation is consequently subject to the usual imprecisions inevitable in any real world experiment. The negative impact of such imprecisions is illustrated for the BB84 QKD protocol. Following this, the main part of this thesis is concerned with the incorporation of such imprecisions in security proofs of the BB84 and two semi-device-independent protocols against the class of collective attacks. On a technical level, by contrast with the vast majority of security proofs developed since the turn of the century, in which recasting the protocol into an equivalent entanglement-based form features heavily in the analysis, the main results obtained here are approached directly from the prepare-and-measure perspective and in particular the connection with the no-cloning theorem and an early security proof by Fuchs et al. against the class of individual attacks is emphasised.<p><p>This thesis also summarises, as an appendix, a separate project which introduces and defines a hierarchy of polytopes intermediate between the local and no-signalling polytopes from the field of Bell nonlocality. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Device-independent cryptography provides security in various tasks whilst removing an assumption that cryptographers previously thought of as crucial -- complete trust in the machinations of their experimental apparatus. The theory of Bell inequalities as a proof of indeterminism within nature allows for secure device-independent schemes requiring neither trust in the cryptographers' devices nor reliance on the completeness of quantum mechanics. However, the extreme paranoia attributable to the relaxed assumptions within device independence requires an explicit consideration of the previously assumed ability of the experimenters to freely make random choices. This thesis addresses the so-called `free will loophole', presenting Bell tests and associated cryptographic protocols robust against adversarial manipulation of the random number generators with which measurements in a Bell test are selected. We present several quantitative measures for this experimental free will, otherwise known as measurement dependence. We discuss how an eavesdropper maliciously preprogramming the experimenters' untrusted devices can falsely simulate the violation of a Bell inequality. We also bound the amount of Bell violation achievable within a certain degree of measurement dependence. This analysis extends to device-independent randomness expansion, bounding the guessing probability and estimating the amount of privacy amplification required to distil private randomness. The protocol is secure against either arbitrary no-signalling or quantum adversaries. We also consider device-independent key distribution, studying adversarial models that exploit the free will loophole. Finally, we examine a model correlated between the random number generators and Bell devices across multiple runs of a Bell test. This enables an explicit exposition of the optimal cheating strategy and how the correlations manifest themselves within this strategy. We prove that there remain Bell violations for a sufficiently high, yet non-maximal degree of measurement dependence which cannot be simulated by a classical attack, regardless of how many runs of the experiment those choices are correlated over.

The device-independent (DI) framework is a novel approach to quantum information science which exploits the nonlocality of quantum physics to certify the correct functioning of a quantum information processing task without relying on any assumption on the inner workings of the devices performing the task. This thesis focuses on the device-independent certification and generation of true randomness for cryptographic applications. The existence of such true randomness relies on a fundamental relation between the random character of quantum theory and its nonlocality, which arises in the context of Bell tests. Device-independent randomness generation (DIRG) and quantum key distribution (DIQKD) protocols usually evaluate the produced randomness (as measured by the conditional min-entropy) as a function of the violation of a given Bell inequality. However, the probabilities characterising the measurement outcomes of a Bell test are richer than the degree of violation of a single Bell inequality. In this work we show that a more accurate assessment of the randomness present in nonlocal correlations can be obtained if the value of several Bell expressions is simultaneously taken into account, or if the full set of probabilities characterising the behaviour of the device is considered. As a side result, we show that to every behaviour there corresponds an optimal Bell expression allowing to certify the maximal amount of DI randomness present in the correlations. Based on these results, we introduce a family of protocols for DIRG secure against classical side information that relies on the estimation of an arbitrary number of Bell expressions, or even directly on the experimental frequencies of the measurement outcomes. The family of protocols we propose also allows for the evaluation of randomness from a subset of measurement settings, which can be advantageous when considering correlations for which some measurement settings result in more randomness than others. We provide numerical examples illustrating the advantage of this method for finite data, and show that asymptotically it results in an optimal generation of randomness from experimental data without having to assume beforehand that the devices violate a specific Bell inequality. / L'approche indépendante des appareils ("device-independent" en anglais) est une nouvelle approche en informatique quantique. Cette nouvelle approche exploite la non-localité de la physique quantique afin de certifier le bon fonctionnement d'une tâche sans faire appel à des suppositions sur les appareils menant à bien cette tâche. Cette thèse traite de la certification et la génération d'aléa indépendante des appareils pour des applications cryptographiques. L'existence de cet aléa repose sur une relation fondamentale entre le caractère aléatoire de la théorie quantique et sa non-localité, mise en lumière dans le cadre des tests de Bell. Les protocoles de génération d'aléa et de distribution quantique de clés indépendants des appareils mesurent en général l'aléa produit en fonction de la violation d'une inégalité de Bell donnée. Cependant les probabilités qui caracterisent les résultats de mesures dans un test de Bell sont plus riches que le degré de violation d'une seule inégalité de Bell. Dans ce travail nous montrons qu'une évaluation plus exacte de l'aléa présent dans les corrélations nonlocales peut être faite si l'on tient compte de plusieurs expressions de Bell à la fois ou de l'ensemble des probabilités (ou comportement) caractérisant l'appareil testé. De plus nous montrons qu'à chaque comportement correspond une expression de Bell optimale permettant de certifier la quantité maximale d'aléa présente dans ces corrélations. À partir de ces resultats, nous introduisons une famille de protocoles de génération d'aléa indépendants des appareils, sécurisés contre des adversaires classiques, et reposant sur l'évaluation de l'aléa à partir d'un nombre arbitraire d'expressions de Bell, ou même à partir des fréquences expérimentales des résultats de mesure. Les protocoles proposés permettent aussi d'évaluer l'aléa à partir d'un sous-ensemble de choix de mesure, ce qui peut être avantageux lorsque l'on considère des corrélations pour lesquelles certains choix de mesure produisent plus d'aléa que d'autres. Nous fournissons des exemples numériques illustrant l'avantage de cette méthode pour des données finies et montrons qu'asymptotiquement cette méthode résulte en un taux de génération d'aléa optimal à partir des données expérimentales, sans devoir supposer à priori que l'expérience viole une inégalité de Bell spécifique. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

L'avènement de l'informatique quantique permet de réétudier les primitives cryptographiques avec une sécurité inconditionnelle, c'est à dire sécurisé même contre des adversaires tout puissants. En 1984, Bennett et Brassard ont construit un protocole quantique de distribution de clé. Dans ce protocole, deux joueurs Alice et Bob coopèrent pour partager une clé secrète inconnue d'une tierce personne Eve. Ce protocole a une sécurité inconditionnelle et n'a pasd'équivalent classique.Dans ma thèse, j'ai étudié les primitives cryptographiques à deux joueurs où ces joueurs ne se font pas confiance. J'étudie principalement le pile ou face quantique et la mise-en-gage quantique de bit. En informatique classique, ces primitivessont réalisables uniquement avec des hypothèses calculatoires, c'est-à-dire en supposant la difficulté d'un problème donné. Des protocoles quantiques ont été construits pour ces primitives où un adversaire peut tricher avec une probabilité constante strictement inférieure à 1, ce qui reste impossible classiquement. Néanmoins, Lo et Chau ont montré l'impossibilité de créer ces primitives parfaitement même en utilisant l'informatique quantique. Il reste donc à déterminer quelles sont les limites physiques de ces primitives.Dans une première partie, je construis un protocole quantique de pile ou face où chaque joueur peut tricher avec probabilité au plus 1/racine(2) + eps pour tout eps > 0. Ce résultat complète un résultat de Kitaev qui dit que dans un jeu de pile ou face quantique, un joueur peut toujours tricher avec probabilité au moins 1/racine(2). J'ai également construit un protocole de mise-en-gage de bit quantique optimal où un joueur peut tricher avec probabilité au plus 0,739 + eps pour tout eps > 0 puis ai montré que ce protocole est en fait optimal. Finalement, j'ai dérivé des bornes inférieures et supérieures pour une autre primitive: la transmission inconsciente, qui est une primitive universelle.Dans une deuxième partie, j'intègre certains aspects pratiques dans ces protocoles. Parfois les appareils de mesure ne donnent aucun résultat, ce sont les pertes dans la mesure. Je construis un protocole de lancer de pièce quantique tolérant aux pertes avec une probabilité de tricher de 0,859. Ensuite, j'étudie le modèle dispositif-indépendant où on ne suppose plus rien sur les appareils de mesure et de création d'état quantique.Finalement, dans une troisième partie, j'étudie ces primitives cryptographiques avec un sécurité computationnelle. En particulier, je fais le lien entre la mise en gage de bit quantique et les protocoles zero-knowledge quantiques. / Quantum computing allows us to revisit the study of quantum cryptographic primitives with information theoretic security. In 1984, Bennett and Brassard presented a protocol of quantum key distribution. In this protocol, Alice and Bob cooperate in order to share a common secret key k, which has to be unknown for a third party that has access to the communication channel. They showed how to perform this task quantumly with an information theoretic security; which is impossible classically.In my thesis, I study cryptographic primitives with two players that do not trust each other. I study mainly coin flipping and bit commitment. Classically, both these primitives are impossible classically with information theoretic security. Quantum protocols for these primitives where constructed where cheating players could cheat with probability stricly smaller than 1. However, Lo, Chau and Mayers showed that these primitives are impossible to achieve perfectly even quantumly if one requires information theoretic security. I study to what extent imperfect protocols can be done in this setting.In the first part, I construct a quantum coin flipping protocol with cheating probabitlity of 1/root(2) + eps for any eps > 0. This completes a result by Kitaev who showed that in any quantum coin flipping protocol, one of the players can cheat with probability at least 1/root(2). I also constructed a quantum bit commitment protocol with cheating probability 0.739 + eps for any eps > 0 and showed that this protocol is essentially optimal. I also derived some upper and lower bounds for quantum oblivious transfer, which is a universal cryptographic primitive.In the second part, I study some practical aspects related to these primitives. I take into account losses than can occur when measuring a quantum state. I construct a Quantum Coin Flipping and Quantum Bit Commitment protocols which are loss-tolerant and have cheating probabilities of 0.859. I also construct these primitives in the device independent model, where the players do not trust their quantum device. Finally, in the third part, I study these cryptographic primitives with information theoretic security. More precisely, I study the relationship between computational quantum bit commitment and quantum zero-knowledge protocols.