Le positionnement d'un engin sous-marin s'appuie sur des systèmes dits "acoustiques". Ces derniers renseignent la position relative de l'engin immergé par rapport au navire support. Les performances de ces systèmes sont définies en termes de limite de portée et de précision. Le principe de ces systèmes repose sur les notions de distance-métrie et de goniométrie, qui s'appuient toutes deux sur l'estimation du temps de propagation et donc de la date d'arrivée du signal utile. Cela est classiquement réalisé par une opération de Compression d'Impulsion. Cette technique qui est largement utilisée dans les domaines du SONAR, RADAR et imagerie bio-médicale, repose sur une application sous-optimale du Filtrage Adapté. En effet, le Filtrage Adapté est une technique d'estimation ou de détection optimale lorsque le bruit et blanc et gaussien et lorsque le signal utile est déterministe, c'est-à-dire que le signal reçu est bien connu. Cependant, il est bien connu que dans le monde sous-marin, le bruit n'est pas blanc, et pas toujours gaussien. Aussi, le signal utile étant déformé soit par le milieu de propagation soit par des phénomènes physiques tels que l'effet Doppler, celui-ci n'est pas déterministe. On peut alors considérer que le bruit est coloré et que le signal utile est une réalisation d'un processus aléatoire. Ainsi, en vue d'étendre les hypothèse d'application de la Compression d'Impulsion classique, nous proposons de construire une nouvelle forme de Compression d'Impulsion basée sur l'utilisation du Filtrage Adapté Stochastique. En effet, ce dernier est une extension naturelle du Filtrage Adapté pour des bruits colorés et des signaux déterministes. Toutefois, le Filtrage Adapté Stochastique suppose que les signaux sont stationnaires au second ordre. Or, cela n'est pas toujours le cas pour le bruit en milieu marin, et cela n'est jamais le cas pour un signal modulé en fréquence tel que ceux utilisés par les systèmes de positionnement acoustiques. Ainsi, nous proposons une nouvelle technique de Compression d'Impulsion alliant les qualités du Filtrage Adapté Stochastique et celle des techniques Temps-Fréquence. Ces dernières, et en particulier la transformée de Wigner-Ville, permettent de contourner l'hypothèse de stationnarité imposée par le Filtrage Adapté Stochastique. D'autre part, en vue de contrer l'apparition d'interférences générées par ces techniques, nous développons ici une approche par " décomposition atomique " sur une base de DCT. Ainsi donc, ces trois années de thèse, ont donné naissance à de nouvelles méthodes de Compression d'Impulsion qui permettent d'améliorer les performances des systèmes de positionnement sous-marin.

This thesis deals with the question of what resources are necessary and sufficient for quantum computational speedup. In particular, we study what resources are required to promote fault tolerant stabilizer computation to universal quantum computation. In this context we discover a remarkable connection between the possibility of quantum computational speedup and negativity in the discrete Wigner function, which is a particular distinguished quasi-probability representation for quantum theory. This connection allows us to establish a number of important results related to magic state computation, an important model for fault tolerant quantum computation using stabilizer operations supplemented by the ability to prepare noisy non-stabilizer ancilla states. In particular, we resolve in the negative the open problem of whether every non-stabilizer resource suffices to promote computation with stabilizer operations to universal quantum computation. Moreover, by casting magic state computation as resource theory we are able to quantify how useful ancilla resource states are for quantum computation, which allows us to give bounds on the required resources. In this context we discover that the sum of the negative entries of the discrete Wigner representation of a state is a measure of its usefulness for quantum computation. This gives a precise, quantitative meaning to the negativity of a quasi-probability representation, thereby resolving the 80 year debate as to whether this quantity is a meaningful indicator of quantum behaviour. We believe that the techniques we develop here will be widely applicable in quantum theory, particularly in the context of resource theories.

University, Diss., 1998--Konstanz.

Techn. Universiẗat, Diss., 2002--Darmstadt.

Neste trabalho formulamos uma versão do princípio variacional de pressão no contexto de operadores densidade em mecânica quântica. Tal princípio relaciona um potencial e um conceito de entropia, que é induzido por um sistema de funções iteradas quântico (QIFS), de forma análoga ao que é feito em formalismo termodinâmico com a entropia métrica do operador shift e um potencial contínuo. Iremos definir um conceito de processo estocástico quântico induzido por tais QIFS de forma natural, e faremos considerações sobre funções de Wigner discretas e certos canais quânticos obtidos no nosso contexto. / In this work we formulate a version of the variational principle of pressure in the context of density operators in quantum mechanics. Such principle relates a potential and a concept of entropy, which is induced by a quantum iterated function system (QIFS), in a way which is analogous to what is done in thermodynamic formalism with the metric entropy of the shift operator and a continuous potential. We will de ne a concept of quantum stochastic process induced by such QIFS in a natural way, and we make some considerations on discrete Wigner functions and certain quantum channels obtained in our setting.

Neste trabalho formulamos uma versão do princípio variacional de pressão no contexto de operadores densidade em mecânica quântica. Tal princípio relaciona um potencial e um conceito de entropia, que é induzido por um sistema de funções iteradas quântico (QIFS), de forma análoga ao que é feito em formalismo termodinâmico com a entropia métrica do operador shift e um potencial contínuo. Iremos definir um conceito de processo estocástico quântico induzido por tais QIFS de forma natural, e faremos considerações sobre funções de Wigner discretas e certos canais quânticos obtidos no nosso contexto. / In this work we formulate a version of the variational principle of pressure in the context of density operators in quantum mechanics. Such principle relates a potential and a concept of entropy, which is induced by a quantum iterated function system (QIFS), in a way which is analogous to what is done in thermodynamic formalism with the metric entropy of the shift operator and a continuous potential. We will de ne a concept of quantum stochastic process induced by such QIFS in a natural way, and we make some considerations on discrete Wigner functions and certain quantum channels obtained in our setting.

Neste trabalho formulamos uma versão do princípio variacional de pressão no contexto de operadores densidade em mecânica quântica. Tal princípio relaciona um potencial e um conceito de entropia, que é induzido por um sistema de funções iteradas quântico (QIFS), de forma análoga ao que é feito em formalismo termodinâmico com a entropia métrica do operador shift e um potencial contínuo. Iremos definir um conceito de processo estocástico quântico induzido por tais QIFS de forma natural, e faremos considerações sobre funções de Wigner discretas e certos canais quânticos obtidos no nosso contexto. / In this work we formulate a version of the variational principle of pressure in the context of density operators in quantum mechanics. Such principle relates a potential and a concept of entropy, which is induced by a quantum iterated function system (QIFS), in a way which is analogous to what is done in thermodynamic formalism with the metric entropy of the shift operator and a continuous potential. We will de ne a concept of quantum stochastic process induced by such QIFS in a natural way, and we make some considerations on discrete Wigner functions and certain quantum channels obtained in our setting.

abstract: Advanced and mature computer simulation methods exist in fluid dynamics, elec- tromagnetics, semiconductors, chemical transport, and even chemical and material electronic structure. However, few general or accurate methods have been developed for quantum photonic devices. Here, a novel approach utilizing phase-space quantum mechanics is developed to model photon transport in ring resonators, a form of en- tangled pair source. The key features the model needs to illustrate are the emergence of non-classicality and entanglement between photons due to nonlinear effects in the ring. The quantum trajectory method is subsequently demonstrated on a sequence of elementary models and multiple aspects of the ring resonator itself. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21550号 / 理博第4457号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 戸塚 圭介, 教授 川上 則雄, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24398号 / 理博第4897号 / 新制||理||1700(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐藤 昌利, 教授 佐々 真一, 准教授 戸塚 圭介 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM