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Galvão, Ernesto Fagundes. "Foundations od quantum theory and quantum information applications." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249255.
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Timpson, Christopher Gordon. "Quantum information theory and the foundations of quantum mechanics." Thesis, University of Oxford, 2004. http://ora.ox.ac.uk/objects/uuid:457a0257-016d-445d-a6b2-f1bdd2648523.
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This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings ‘information’ functions as an abstract noun, hence does not refer to a particular or substance. The popular claim ‘Information is Physical’ is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske’s (1981) attempt to base a semantic notion of information on ideas from information theory. The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of recognising the logical status of ‘information’ as an abstract noun: it is argued that the conceptual puzzles often associated with this phenomenon result from the familiar error of hypostatizing an abstract noun. The approach of Deutsch and Hayden (2000) to the questions of locality and information flow in entangled quantum systems is assessed. It is suggested that the approach suffers from an equivocation between a conservative and an ontological reading; and the differing implications of each is examined. Some results are presented on the characterization of entanglement in the Deutsch-Hayden formalism. Part I closes with a discussion of some philosophical aspects of quantum computation. In particular, it is argued against Deutsch that the Church-Turing hypothesis is not underwritten by a physical principle, the Turing Principle. Some general morals are drawn concerning the nature of quantum information theory. In Part II, attention turns to the question of the implications of quantum information theory for our understanding of the meaning of the quantum formalism. Following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger’s (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.
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Kestin, Gregory Michael. "Light-Shell Theory Foundations." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11596.
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We study the motivation and groundwork for the construction of a Light-Shell Effective Theory, an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We begin in chapter 2 with a simple electrodynamics calculation to motivate the picture of the ``light-shell," in which all electric and magnetic fields lie on a spherical shell that moves outward at the speed of light. The result turns out to do more than motivate, as it also hints at an important feature of the theory, namely the gauge in which we subsequently choose to do calculations, called Light-Shell Gauge.<br>Physics
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Wallace, David. "Issues in the foundations of relativistic quantum theory." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270178.
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Fernandes, Marco Cezar Barbosa. "Geometric algebras and the foundations of quantum theory." Thesis, Birkbeck (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.283390.
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The difficulties associated with the quantization of the gravitational field suggests a modification of space-time is needed. For example at suffici~ly small length scales the geometry of space-time might better discussed in terms of a noncommutative algebra. In this thesis we discuss a particular example of a noncommutative algebra, namely the symplectic Schonberg algebra, which we treat as a geometric algebra. Thus our investigation has some features in common with recent work that explores how geometry can be formulated in terms of noncommutative structures. The symplectic Schonberg algebra is a geometric algebra associated with the covariant and the contravariant vectors of a general affine space. The "embedding" of this space in a noncommutative algebra leads us to a structure which we regard as a noncommutative affine geometry. The theory in question takes us naturally to stochastic elements without the usual ad-hoc assumptions concerning measurements in physical ensembles that are made in the usual interpretation of quantum mechanics. The probabilistic nature of space is obtained purely from the structure of this algebra. As a consequence, geometric objects like points, lines and etc acquire a kind of fuzzy character. This allowed us to construct the space of physical states within the algebra in terms of its minimum left-ideals as was proposed by Hiley and Frescura [1J. The elements of these ideals replace the ordinary point in the Cartesian geometry. The study of the main inner-automorphisms of the algebra gives rise to the representation of the symplectic group of linear classical canonical transformations. We show that this group acts on the minimum left-ideal of the algebra and in this case manifests itself as the metaplectic group, i.e the double covering of the symplectic group. Thus we are lead to the theory of symplectic spinors as minimum left-ideals in exactly the same way as the orthogonal spinors can be formulated in terms of minimum left-ideals in the Clifford algebra .. The theory of the automorphisms of the symplectic Schonberg algebra allows us to give a geometrical meaning to integral transforms such as: the Fourier transform, the real and complex Gauss Weierstrass transform, the Bargmann (3) transform and the Bilateral Laplace transform. We construct a technique for obtaining a realization of these algebraic transformations in terms of integral kernels. This gives immediately the Feynmann propagators of conventional non-relativistic quantum mechanics for Hamiltonians quadratic in momentum and position. This then links our approach to those used in quantum mechanics and optics. The link between the theory of this noncommutative geometric algebra and the theory of vector bundles is also discussed.
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Arafat, Sachi. "Foundations research in information retrieval inspired by quantum theory." Thesis, Connect to e-thesis, 2008. http://theses.gla.ac.uk/181/.
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Thesis (Ph.D.) - University of Glasgow, 2007.<br>Ph.D. thesis submitted to the Department of Computer Science, Faculty of Information and Mathematical Sciences, University of Glasgow, 2007. Includes bibliographical references. Print version also available.
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Saunders, Simon Wolfe. "The mathematical and philosophical foundations of quantum field theory." Thesis, King's College London (University of London), 1988. https://kclpure.kcl.ac.uk/portal/en/theses/the-mathematical-and-philosophical-foundations-of-quantum-field-theory(a36b5ec8-40ae-4ea6-98e3-4c81592a18e0).html.
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The thesis is primarily concerned with these objectives: to say what is a quantum field theory, and to explain why and how relativistic quantum field theory differs from non-relativistic quantum field theory, even in the free or weakly interacting (quasi-free) case. Following the ideas of Irving Segal, I shall establish that in this case there is an essential identity in structure of the non-relativistic and relativistic field theories. Novel but straightforward applications of this theory are made to the complex scalar field,and in relation to t.he Dirac hole theory. Although the structure of the relativistic and non-relativistic quasi-free theories is essentially identical, the concept of localization finds different expressions. This plays a fundamental role when interactions are introduced, and leads to two quite distinct notions of causality. I shall confine the detailed study to the massive scalar and spin 1/2 linear field theories, for the most part in the quasi-free case. Not even the latter are trivial, for they descri,be the observed phenomenology and are therefore of central empistemological importance to relativistic quantum theory. I al so advance a general interpretat i ve framework for the philosophical analysis of quantum theory. This is essent ially a real ist interpretation founded on abstract • C -algebras, and it is applied to the measurement problem. The physical and mathematical theories that I draw upon are developed in a historical context. The mathematical theory is presented in a largely heuristic way.
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Allen, John-Mark. "Reality, causality, and quantum theory." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:01413eef-0944-4ec5-ad53-ac8378bcf4be.
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Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a reimagining of what fundamental reality, or 'ontology', could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. The way that quantum theory describes the state of a system is one of its most unintuitive features. It is natural, therefore, to ask whether a similarly strange description of states is required on an ontological level. This thesis proves that almost all quantum superposition states for d > 3 dimensions must be real - that is, present in the ontology in a well-defined sense. This is a strong requirement which prevents intuitive explanations of the many quantum phenomena which are based on superpositions. A new theorem is also presented showing that quantum theory is incompatible with macro-realist ontologies, where certain physical quantities must always have definite values. This improves on the Leggett-Garg argument, which also aims to prove incompatibility with macro-realism but contains loopholes. Variations on both of these results that are error-tolerant (and therefore amenable to experimentation) are presented, as well as numerous related theorems showing that the ontology of quantum states must be somewhat similar to the quantum states themselves in various specific ways. Extending these same methods to quantum communication, a simple proof is found showing that an exponential number of classical bits are required to communicate a linear number of qubits. That is, classical systems are exponentially bad at storing quantum data. Causal influences are another part of ontology where quantum theory demands a revision of our classical notions. This follows from the outcomes of Bell experiments, as rigorously shown in recent analyses. Here, the task of constructing a native quantum framework for reasoning about causal influences is tackled. This is done by first analysing the simple example of a common cause, from which a quantum version of Reichenbach's principle is identified. This quantum principle relies on an identification of quantum conditional independence which can be defined in four ways, each naturally generalising a corresponding definition for classical conditional independence. Not only does this allow one to reason about common causes in a quantum experiments, but it can also be generalised to a full framework of quantum causal models (mirroring how classical causal models generalise Reichenbach's principle). This new definition of quantum causal models is illustrated by examples and strengthened by it's foundation on a robust quantum Reichenbach's principle. An unusual, but surprisingly fruitful, setting for considering quantum ontology is found by considering time travel to the past. This provides a testbed for different ontological concepts in quantum theory and new ways to compare classical and quantum frameworks. It is especially useful for comparing computational properties. In particular, time travel introduces non-linearity to quantum theory, which brings (sometimes implicit) ontological assumptions to the fore while introducing strange new abilities. Here, a model for quantum time travel is presented which arguably has fewer objectionable features than previous attempts, while remaining similarly well-motivated. This model is discussed and compared with previous quantum models, as well as with the classical case. Together, these threads of investigation develop a better understanding of how quantum theory affects possible ontologies and how ontological prejudices influence quantum theory.
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Carruth, Nathan Thomas. "Classical Foundations for a Quantum Theory of Time in a Two-Dimensional Spacetime." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/708.
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We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.
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Al-Safi, Sabri Walid. "Quantum theory from the perspective of general probabilistic theories." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247218.
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This thesis explores various perspectives on quantum phenomena, and how our understanding of these phenomena is informed by the study of general probabilistic theories. Particular attention is given to quantum nonlocality, and its interaction with areas of physical and mathematical interest such as entropy, reversible dynamics, information-based games and the idea of negative probability. We begin with a review of non-signaling distributions and convex operational theories, including “black box” descriptions of experiments and the mathematics of convex vector spaces. In Chapter 3 we derive various classical and quantum-like quasiprobabilistic representations of arbitrary non-signaling distributions. Previously, results in which the density operator is allowed to become non-positive [1] have proved useful in derivations of quantum theory from physical requirements [2]; we derive a dual result in which the measurement operators instead are allowed to become non-positive, and show that the generation of any non-signaling distribution is possible using a fixed separable state with negligible correlation. We also derive two distinct “quasi-local” models of non-signaling correlations. Chapter 4 investigates non-local games, in particular the game known as Information Causality. By analysing the probability of success in this game, we prove the conjectured tightness of a bound given in [3] concerning how well entanglement allows us to perform the task of random access coding, and introduce a quadratic bias bound which seems to capture a great deal of information about the set of quantum-achievable correlations. By reformulating Information Causality in terms of entropies, we find that a sensible measure of entropy precludes many general probabilistic theories whose non-locality is stronger than that of quantum theory. Chapter 5 explores the role that reversible transitivity (the principle that any two pure states are joined by a reversible transformation) plays as a characteristic feature of quantum theory. It has previously been shown that in Boxworld, the theory allowing for the full set of non-signaling correlations, any reversible transformation on a restricted class of composite systems is merely a composition of relabellings of measurement choices and outcomes, and permutations of subsystems [4]. We develop a tabular description of Boxworld states and effects first introduced in [5], and use this to extend this reversibility result to any composite Boxworld system in which none of the subsystems are classical.
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Rådmark, Magnus. "Photonic quantum information and experimental tests of foundations of quantum mechanics." Doctoral thesis, Stockholms universitet, Fysikum, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-37464.
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Entanglement is a key resource in many quantum information schemes and in the last years the research on multi-qubit entanglement has drawn lots of attention. In this thesis the experimental generation and characterisation of multi-qubit entanglement is presented. Specifically we have prepared entangled states of up to six qubits. The qubits were implemented in the polarisation degree of freedom of single photons. We emphasise that one type of states that we produce are rotationally invariant states, remaining unchanged under simultaneous identical unitary transformations of all their individual constituents. Such states can be applied to e.g. decoherence-free encoding, quantum communication without sharing a common reference frame, quantum telecloning, secret sharing and remote state preparation schemes. They also have properties which are interesting in studies of foundations of quantum mechanics. In the experimental implementation we use a single source of entangled photon pairs, based on parametric down-conversion, and extract the first, second and third order events. Our experimental setup is completely free from interferometric overlaps, making it robust and contributing to a high fidelity of the generated states. To our knowledge, the achieved fidelity is the highest that has been observed for six-qubit entangled states and our measurement results are in very good agreement with predictions of quantum theory. We have also performed another novel test of the foundations of quantum mechanics. It is based on an inequality that is fulfilled by any non-contextual hidden variable theory, but can be violated by quantum mechanics. This test is similar to Bell inequality tests, which rule out local hidden variable theories as possible completions of quantum mechanics. Here, however, we show that non-contextual hidden variable theories cannot explain certain experimental results, which are consistent with quantum mechanics. Hence, neither of these theories can be used to make quantum mechanics complete.
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Lee, Ciaran M. "Bounds on computation from physical principles." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:39451e29-3719-4cf4-a030-57c07e603380.
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The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This raises the general question of what broad relationships exist between physical principles and computation. The current thesis explores this question within the operationally-defined framework of generalised probabilistic theories. In particular, we investigate the limits on computational power imposed by simple physical principles. At present, the best known upper bound on the power of quantum computers is that <b>BQP</b> is contained in <b>AWPP</b>, where <b>AWPP</b> is a classical complexity class contained in PP. We define a circuit-based model of computation in the above mentioned operational framework and show that in theories where local measurements suffice for tomography, efficient computations are also contained in <b>AWPP</b>. Moreover, we explicitly construct a theory in which the class of efficiently solvable problems exactly equals <b>AWPP</b>, showing this containment to be tight. We also investigate how simple physical principles bound the power of computational paradigms which combine computation and communication in a non-trivial fashion, such as interactive proof systems. Additionally, we show how some of the essential components of computational algorithms arise from certain natural physical principles. We use these results to investigate the relationship between interference behaviour and computational power, demonstrating that non-trivial interference behaviour is a general resource for post-classical computation. We then investigate whether post-quantum interference is a resource for post-quantum computation. Sorkin has defined a hierarchy of possible post-quantum interference behaviours where, informally, the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. In quantum theory, at most pairs of paths can ever interact in a fundamental way. We consider how Grover's speed-up depends on the order of interference in a theory, and show that, surprisingly, the quadratic lower bound holds regardless of the order of interference.
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Solanki, Vinesh. "Zariski structures in noncommutative algebraic geometry and representation theory." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45.
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A suitable subcategory of affine Azumaya algebras is defined and a functor from this category to the category of Zariski structures is constructed. The rudiments of a theory of presheaves of topological structures is developed and applied to construct examples of structures at a generic parameter. The category of equivariant algebras is defined and a first-order theory is associated to each object. For those theories satisfying a certain technical condition, uncountable categoricity and quantifier elimination results are established. Models are shown to be Zariski structures and a functor from the category of equivariant algebras to Zariski structures is constructed. The two functors obtained in the thesis are shown to agree on a nontrivial class of algebras.
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Garner, Andrew J. P. "Phase and interference phenomena in generalised probabilistic theories." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:c0017faf-cbe0-4365-a1ff-080fa031d006.
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Phase lies at the heart of quantum physics and quantum information theory. A quantum bit is qualitatively different from a classical bit as it allows for the coherent superposition of possibilities, which demonstrate different behaviours depending on the phase between them. These behaviours constitute as interference phenomena, and lie behind the existence of algorithms in quantum computing which are arguably faster than the best classical alternatives. The concept of phase is deeply steeped in the structure of Hilbert spaces: the mathematical framework that underlies quantum theory. What if quantum theory did not hold in all scenarios, or was only a limiting case of some broader theory? In this case, would we still be able to meaningfully talk about phase and interference? In this thesis, we will adopt an operational generalisation of quantum theory known as the framework of generalised probabilistic theories. We will provide a reasonable definition of phase in this framework. Using this, we shall explore single-particle interferometry set-ups (particularly Mach-Zehnder interferometers): experiments whose output is highly dependent on the phase between the spatially disjoint branches through which a particle might be traversing. By applying physically-motivated locality considerations, we identify the crucial role that the uncertainty principle and its generalisations play in quantum theory as an enabler of non-trivial interference. By taking into account relativity of simultaneity, we will also provide a physical motivation for why standard quantum theory provides the best description of the location of a particle traversing such a system. Finally, we apply our generalised definition of phase in the related context of particle exchange behaviour, and identify a method for classifying post-quantum particles. All of this will demonstrate that phase between possibilities and its consequences are not uniquely quantum phenomena. Much of the behaviour we might ascribe to phase in quantum theory in fact holds generally true for phase in probabilistic theories.
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Atzemoglou, George Philip. "Higher-order semantics for quantum programming languages with classical control." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:9fdc4a26-cce3-48ed-bbab-d54c4917688f.
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This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation: Quantum Key Distribution, the quantum Fourier transform, and the teleportation protocol.
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Durham, Ian T. "Sir Arthur Eddington and the foundations of modern physics." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/12933.
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In this dissertation I analyze Sir Arthur Eddington's statistical theory as developed in the first six chapters of his posthumously published Fundamental Theory. In particular I look at the mathematical structure, philosophical implications, and relevancy to modern physics. This analysis is the only one of Fundamental Theory that compares it to modern quantum field theory and is the most comprehensive look at his statistical theory in four decades. Several major insights have been made in this analysis including the fact that he was able to derive Pauli's Exclusion Principle in part from Heisenberg's Uncertainty Principle. In addition the most profound general conclusion of this research is that Fundamental Theory is, in fact, an early quantum field theory, something that has never before been suggested. Contrary to the majority of historical reports and some comments by his contemporaries, this analysis shows that Eddington's later work is neither mystical nor was it that far from mainstream when it was published. My research reveals numerous profoundly deep ideas that were ahead of their time when Fundamental Theory was developed, but that have significant applicability at present. As such this analysis presents several important questions to be considered by modern philosophers of science, physicists, mathematicians, and historians. In addition it sheds new light on Eddington as a scientist and mathematician, in part indicating that his marginalization has been largely unwarranted.
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Duprey, Quentin. "Valeurs Faibles, Trajectoires Faibles et Interferométrie." Thesis, Cergy-Pontoise, 2019. http://www.theses.fr/2019CERG1049.
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La théorie de la mesure, basée sur la mesure projective, constitue un aspect fondamental de la mécanique quantique. La mesure faible diffère de la mesure projective traditionnelle sur laquelle les axiomes élémentaires de la physique quantique sont bâtis. Bien que définie dans le cadre de la théorie quantique standard, les mesures faibles sont encore mal comprises. Le travail de thèse s'inscrit dans une large démarche qui vise à comprendre les implications conceptuelles et pratiques d'une telle mesure et à la comprendre dans le cadre de la théorie quantique.Le chapitre 1 est une introduction détaillée à la mesure faible et à la valeur faible. Ensuite, nous étudierons les "trajectoires faibles" dans un interféromètre à fentes d'Young. Nous abordons au chapitre 3 les implications de l'annulation d'une valeur faible au regard de l'apparition de trajectoires faibles dans des interféromètres de Mach-Zender imbriqués. Enfin, le chapitre 4 traite des critiques théoriques et expérimentales présentes dans la littérature concernant l'effet du Chat du Cheshire quantique qui est défini dans le cadre de mesures faibles<br>Measurement theory, based on projective measurements, is a fundamental aspect of quantum mechanics. Weak measurements differ from standard projective measurements on which the elementary axioms of quantum physics are built. Although weak measurement framework is defined within standard quantum mechanics, its implications are still poorly understood. The thesis work is part of a broad reflexion that aims to understand the conceptual and practical implications of such a measurement and to understand it in the context of quantum theory.Chapter 1 is a detailed introduction to weak measurements and weak values. Next, we will study the "weak trajectories" in a two slit interferometer. In Chapter 3, we discuss the implications of a cancellation of a weak value with respect to the observation of weak trajectories in nested Mach-Zender interferometers. Finally, Chapter 4 deals with the theoretical and experimental criticisms in the literature of the effect of the Cheshire Cat that is defined in the framework of weak measurement
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Amselem, Elias. "Dynamics of Quantum Correlations with Photons : Experiments on bound entanglement and contextuality for application in quantum information." Doctoral thesis, Stockholms universitet, Fysikum, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-66469.
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The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation.<br><p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Submitted. Paper 5: Submitted. Paper 6: Submitted.</p>
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Hatifi, Mohamed. "Beyond pilot wave dynamics : non-linearity and non-equilibrium in quantum mechanics." Thesis, Ecole centrale de Marseille, 2019. http://www.theses.fr/2019ECDM0006.
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La mécanique quantique a modifié notre façon d'interpréter ce que jadis l'on appelait communément "réalité physique". A titre d'exemple, selon l'interprétation standard de la mécanique quantique (dite interprétation probabiliste de Copenhague) les propriétés d’un objet quantique n'ont pas de réalité physique, du moins, pas avant que l’observateur ne les mesure. De plus, tout semble se passer comme s'il y avait un indéterminisme intrinsèque à la dynamique quantique qui ne permettrait pas de prédire avec certitude le résultat d'une mesure. Dès lors, plusieurs interprétations physiques et philosophiques ont vu naissance afin de décrire (notre connaissance de) cette réalité.C'est au cours de la conférence de Solvay en 1927 que Louis de Broglie, un opposant à l'interprétation probabiliste, proposa une solution alternative qui permettait d'une part de restaurer le déterminisme (ainsi que le réalisme) et d'autre part de remettre au premier plan la notion de trajectoire. Par la suite cette théorie fut redécouverte et complétée par David Bohm pour donner naissance à la théorie connue aujourd'hui sous l'appellation de théorie de l'onde pilote. John Bell a dit à propos de cette interprétation : " En 1952, l'impossible a été rendu possible. C'était dans l'article de David Bohm. Bohm a montré explicitement comment une description indéterministe pouvait être transformée en théorie déterministe."Les travaux présentés dans ce manuscrit de thèse s'inscrivent dans la continuité de la vision de de Broglie et consistent en deux parties, chacune d'elles ayant pour but de répondre à une problématique particulière. Dans la première, on considère deux formalismes du type onde pilote, une version déterministe (dynamique de de Broglie-Bohm chapitre 2) ainsi qu'une de ses extensions stochastiques (dynamique de Bohm-Hiley-Nelson chapitre 3). On s'attardera notamment sur l’émergence de la probabilité quantique à partir de ces dynamiques dans l’approche dite du "Quantum Non-Equilibrium". Cette approche permet entre autres de s'affranchir du statut axiomatique de la distribution de probabilité mais aussi de la justifier par des arguments similaires à ceux que l'on retrouve en mécanique statistique. Parmi ces arguments on retrouvera à titre d’exemple la notion d’ergodicité, de chaos, de mixing ainsi que d’autres propriétés qui feront l’objet d’une étude approfondie (chapitre 4). En particulier, l’émergence de l’équilibre s'accompagne d'un processus de relaxation que nous allons caractériser dans chacune de ces dynamiques (dans le chapitre 3 nous dériverons un théorème H qui décrit quantitativement ce processus dans le cas stochastique). Par ailleurs, nous nous efforcerons, dans une approche phénoménologique, d’appliquer ces théories quantiques d'onde pilote à la dynamique macroscopique des gouttes d'huile rebondissantes dans un bain (chapitre 5).La deuxième problématique quant à elle, repose sur une hypothétique généralisation non-linéaire de la mécanique quantique. En particulier, nous considérerons l'équation de Schrodinger Newton comme une première proposition a cette généralisation. Cette équation non-linéaire découle d’une approximation semi-classique de la gravité et a été entre autres proposée par Roger Penrose pour expliquer le collapse de la fonction d’onde. Nous montrerons dans un premier temps comment le programme de la double solution de Louis de Broglie se développe dans ce contexte (chapitre 6). Par la suite nous verrons comment tester cette généralisation non-linéaire par deux propositions expérimentales (chapitre 7). En particulier, l’une de ces propositions nous conduira à étudier des effets de décohérence lors du refroidissement laser (Doppler cooling, chapitre 8). Pour cela on utilisera le modèle de Ghirardi–Rimini–Weber (GRW) comme modèle de décohérence. Ce qui nous permettra par la suite de généraliser les résultats obtenus auparavant par GRW dans leur modèle<br>The quantum theory has modified the way we interpret what in the past was commonly called "physical reality". As an example, according to the standard interpretation of quantum mechanics (the so-called probabilistic interpretation of Copenhagen), the properties of a quantum object have no physical reality, at least not before the observer measures them. Moreover, everything seems to happen as if there was an intrinsic indeterminism in the quantum dynamics that forbids to predict with certainty the result of a measurement. From then, several physical and philosophical interpretations were born to describe (our knowledge of) this reality.It is in 1927, during the Solvay conference, that Louis de Broglie, an opponent of the probabilistic interpretation, proposed an alternative solution to that problem. He proposed on the one hand to restore determinism (as well as realism) and on the other hand to bring back the notion of trajectory to the foreground. Subsequently this theory was rediscovered and supplemented by David Bohm to give birth to the theory known today as pilot wave theory. John Bell said about this interpretation: " In 1952, I saw the impossible done. It was in papers by David Bohm. Bohm showed explicitly how .... the indeterministic description could be transformed into a deterministic one."The works carried out in this manuscript are in continuity with de Broglie’s view and can be summed up in two main parts, each of them having the aim of answering a particular problem. In the first part, we consider two versions of the pilot wave theory: a deterministic version (de Broglie-Bohm dynamics in chapter 2) as well as one of its stochastic extensions (Bohm-Hiley-Nelson dynamics in chapter 3). In the framework of what is called the "Quantum non-equilibrium" approach we shall see how the quantum probability emerges from those dynamics. This approach makes it possible to get rid of the axiomatic status of the probability distribution but also to justify it by arguments similar to those found in statistical mechanics. Among these arguments we shall for instance find ergodicity, chaos, mixing and other properties that will be studied in depth (chapter 4). In particular, the emergence of the quantum probability is accompanied by a relaxation process that will be characterized for both dynamics (in chapter 3 we derive a strong H-theorem for the stochastic dynamics which quantitatively describes how this process occurs). In addition, we will try in a phenomenological approach to apply these quantum pilot wave theories to the macroscopic dynamics of bouncing oil droplets (chapter 5).The second problem is linked to a hypothetical nonlinear generalization of the quantum theory. In particular, we considered the Schrodinger Newton equation as a first proposal to this generalization. In a nutshell, this non-linear equation derives from a semi-classical approximation of gravity and has been proposed by Roger Penrose among others to explain the collapse of the wave function. We shall first show how it is related to the double solution program of Louis de Broglie (chapter 6). Subsequently we will see how to test this nonlinear generalization by considering two experimental proposals (chapter 7). In particular, one of these proposals will lead us to study the interplay between decoherence and Doppler cooling (chapter 8). To do this we shall use the model of Ghirardi-Rimini and Weber (GRW) as a decoherence model, which will allow us to generalize their original results
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Merry, Alexander. "Reasoning with !-graphs." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:416c2e6d-2932-4220-8506-50e6b403b660.
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The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can be built on this to allow the formalisation of inductive proofs in the string diagrams of compact closed and traced symmetric monoidal categories. String diagrams provide an intuitive method for reasoning about monoidal categories. However, this does not negate the ability for those using them to make mistakes in proofs. To this end, there is a project (Quantomatic) to build a proof assistant for string diagrams, at least for those based on categories with a notion of trace. The development of string graphs has provided a combinatorial formalisation of string diagrams, laying the foundations for this project. The prevalence of commutative Frobenius algebras (CFAs) in quantum information theory, a major application area of these diagrams, has led to the use of variable-arity nodes as a shorthand for normalised networks of Frobenius algebra morphisms, so-called "spider notation". This notation greatly eases reasoning with CFAs, but string graphs are inadequate to properly encode this reasoning. This dissertation firstly extends string graphs to allow for variable-arity nodes to be represented at all, and then introduces !-box notation – and structures to encode it – to represent string graph equations containing repeated subgraphs, where the number of repetitions is abitrary. This can be used to represent, for example, the "spider law" of CFAs, allowing two spiders to be merged, as well as the much more complex generalised bialgebra law that can arise from two interacting CFAs. This work then demonstrates how we can reason directly about !-graphs, viewed as (typically infinite) families of string graphs. Of particular note is the presentation of a form of graph-based induction, allowing the formal encoding of proofs that previously could only be represented as a mix of string diagrams and explanatory text.
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Horsman, Clare Cecilia. "Quantum information and the foundations of quantum mechanics." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.439543.
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Ranchin, Andre. "Alternative theories in quantum foundations." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/52462.
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Abstraction is an important driving force in theoretical physics. New insights often accompany the creation of physical frameworks which are both comprehensive and parsimonious. In particular, the analysis of alternative sets of theories which exhibit similar structural features as quantum theory has yielded important new results and physical understanding. An important task is to undertake a thorough analysis and classification of quantum-like theories. In this thesis, we take a step in this direction, moving towards a synthetic description of alternative theories in quantum foundations. After a brief philosophical introduction, we give a presentation of the mathematical concepts underpinning the foundations of physics, followed by an introduction to the foundations of quantum mechanics. The core of the thesis consists of three results chapters based on the articles in the author’s publications page. Chapter 4 analyses the logic of stabilizer quantum mechanics and provides a complete set of circuit equations for this sub-theory of quantum mechanics. Chapter 5 describes how quantum-like theories can be classified in a periodic table of theories. A pictorial calculus for alternative physical theories, called the ZX calculus for qudits, is then introduced and used as a tool to depict particular examples of quantum-like theories, including qudit stabilizer quantum mechanics and the SpekkensSchreiber toy theory. Chapter 6 presents an alternative set of quantum-like theories, called quantum collapse models. A novel quantum collapse model, where the rate of collapse depends on the Quantum Integrated Information of a physical system, is introduced and discussed in some detail. We then conclude with a brief summary of the main results.
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Leung, Calvin. "Quantum Foundations with Astronomical Photons." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/98.
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Theoretical work in quantum information has demonstrated that a classical hidden-variable model of an entangled singlet state can explain nonclassical correlations observed in tests of Bell’s inequality if while measuring the Bell correlation, the underlying probability distribution of the hidden-variable changes depending on the measurement basis. To rule out this possibility, distant quasars can be utilized as random number generators to set measurement bases in an experimental test of Bell’s inequality. Here we report on the design and characterization of a device that uses the color of incoming quasar photons to output a random bit with nanosecond latency. Through the 1-meter telescope at JPL Table Mountain Observatory, we observe and generate random bits from quasars with redshifts z = 0.1−3.9. In addition, we formulate a mathematical model that quantifies the fidelity of the bits generated.
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Torre, Carazo Gonzalo de la. "From quantum foundations to quantum information protocols and back." Doctoral thesis, Universitat Politècnica de Catalunya, 2015. http://hdl.handle.net/10803/319442.
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Physics has two main ambitions: to predict and to understand. Indeed, physics aims for the prediction of all natural phenomena. Prediction entails modeling the correlation between an action, the input, and what is subsequently observed, the output.Understanding, on the other hand, involves developing insightful principles and models that can explain the widest possible varietyof correlations present in nature. Remarkably, advances in both prediction and understanding foster our physical intuition and, as a consequence, novel and powerful applications are discovered. Quantum mechanics is a very successful physical theory both in terms of its predictive power as well as in its wide applicability. Nonetheless and despite many decades of development, we do not yet have a proper physical intuition of quantum phenomena. I believe that improvements in our understanding of quantum theory will yield better, and more innovative, protocols and vice versa.This dissertation aims at advancing our understanding and developing novel protocols. This is done through four approaches. The first one is to study quantum theory within a broad family of theories. In particular, we study quantum theory within the family of locally quantum theories. We found out that the principle that singles out quantum theory out of this family, thus connecting quantum local and nonlocal structure, is dynamical reversibility. This implies that the viability of large scale quantum computing can be based on concrete physical principles that can be experimentally tested at a local level without needing to test millions of qubits simultaneously. The second approach is to study quantum correlations from a black box perspective thus making as few assumptions as possible. The strategy is to study the completeness of quantum predictions by benchmarking them against alternative models. Three main results and applications come out of our study. Firstly, we prove that performing complete amplification of randomness starting from a source of arbitrarily weak randomness - a task that is impossible with classical resources - is indeed possible via nonlocality. This establishes in our opinion the strongest evidence for a truly random event in nature so far. Secondly, we prove that there exist finite events where quantum theory gives predictions as complete as any no-signaling theory can give, showing that the completeness of quantum theory is not an asymptotic property. Finally, we prove that maximally nonlocal theories can never be maximally random while quantum theory can, showing a trade-off between the nonlocality of a theory and its randomness capabilities. We also prove that quantum theory is not unique in this respect. The third approach we follow is to study quantum correlations in scenarios where some parties have a restriction on the available quantum degrees of freedom. The future progress of semi-device-independent quantum information depends crucially on our ability to bound the strength of these correlations. Here we provide a full characterization via a complete hierarchy of sets that approximate the target set from the outside. Each set can be in turn characterized using standard numerical techniques. One application of our work is certifying multidimensional entanglement device-independently.The fourth approach is to confront quantum theory with computer science principles. In particular, we establish two interesting implications for quantum theory results of raising the Church-Turing thesis to the level of postulate. Firstly, we show how different preparations of the same mixed state, indistinguishable according to the quantum postulates, become distinguishable when prepared computably. Secondly, we identify a new loophole for Bell-like experiments: if some parties in a Bell-like experiment use private pseudorandomness to choose their measurement inputs, the computational resources of an eavesdropper have to be limited to observe a proper violation of non locality.<br>La física tiene dos finalidades: predecir y comprender. En efecto, la física aspira a poder predecir todos los fenómenos naturales. Predecir implica modelar correlaciones entre una acción y la reacción subsiguiente.Comprender, implica desarrollar leyes profundas que expliquen la más amplia gama de correlaciones presentes en la naturaleza. Avances tanto en la capacidad de predicción como en nuestra comprensión fomentan la intuición física y, como consecuencia, surgen nuevas y poderosas aplicaciones. La mecánica cuántica es una teoría física de enorme éxito por su capacidad de predicción y amplia aplicabilidad.Sin embargo, a pesar de décadas de gran desarrollo, no poseemos una intuición física satisfactoria de los fenómenos cuánticos.Creo que mejoras en nuestra comprensión de la teoría cuántica traerán consigo mejores y más innovadores protocolos y vice versa.Ésta tesis doctoral trata simultáneamente de avanzar nuestra comprensión y de desarrollar nuevos protocolos mediante cuatro enfoques distintos.El primero consiste en estudiar la mecánica cuántica como miembro de una familia de teorías: las teorías localmente cuánticas. Probamos que el principio que selecciona a la mecánica cuántica, conectando por tanto la estructura cuántica local y no local, es la reversibilidad de su dinámica.Ésto implica que la viabilidad de la computación cuántica a gran escala puede ser estudiada de manera local, comprobando experimentalmente ciertos principios físicos. El segundo enfoque consiste en estudiar las correlaciones cuánticas desde una perspectiva de 'caja negra', haciendo así el mínimo de asunciones físicas. La estrategia consiste en estudiar la completitud de las predicciones cuánticas, comparándolas con todos los modelos alternativos. Hemos obtenido tres grandes resultados. Primero, probamos que se puede amplificar completamente la aleatoriedad de una fuente de aleatoriedad arbitrariamente débil.Ésta tarea, imposible mediante recursos puramente clásicos, se vuelve factible gracias a la no localidad. Ésto establece a nuestro parecer la evidencia más fuerte de la existencia de eventos totalmente impredecibles en la naturaleza. Segundo, probamos que existen eventos finitos cuyas predicciones cuánticas son tan completas como permite el principio de 'no signaling'. Ésto prueba que la completitud de la mecánica cuántica no es una propiedad asintótica. Finalmente, probamos que las teorías máximamente no locales no pueden ser máximamente aleatorias, mientras que la mecánica cuántica lo es. Ésto muestra que hay una compensación entre la no localidad de una teoría y su capacidad para generar aleatoriedad. También probamos que la mecánica cuántica no es única en éste respecto. En tercer lugar, estudiamos las correlaciones cuánticas en escenarios dónde algunas partes tienen restricciones en el número de grados de libertad cuánticos accesibles. Éste escenario se denomina 'semi-device-independent'. Aquí encontramos una caracterización completa de éstas correlaciones mediante una jerarquía de conjuntos que aproximan al conjunto buscado desde fuera y que pueden ser caracterizados a su vez mediante técnicas numéricas estandar. Un aplicación de nuestro trabajo es la certificación de entrelazamiento multidimensional de manera 'device-independent'. El cuarto y último enfoque consiste en enfrentar a la mecánica cuántica con principios provenientes de la computación. En particular, establecemos dos implicaciones para la mecánica cuántica de elevar la tesis de Church-Turing al nivel de postulado. Primero, mostramos que diferentes preparaciones de un mismo estado mixto, indistinguibles de acuerdo a los axiomas cuánticos, devienen distinguibles cuando son preparados de manera computable. Segundo, identificamos un nuevo 'loophole' en experimentos de Bell: si algunas partes en un experimento de Bell usan pseudo aleatoriedad para escoger sus medidas, los recursos computacionales de un espía deben ser limitados a fin de observar verdaderamente la no localidad.
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Schreckenberg, Stephan Reinhold. "Structural foundations of quantum history theories." Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309236.
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Fearns, John David. "Foundations of quantum physics in smooth toposes." Thesis, Imperial College London, 2003. http://hdl.handle.net/10044/1/12011.
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Yadin, Benjamin. "Resource theories of quantum coherence : foundations and applications." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:facfa689-d474-4bdf-9ef6-a43d1b1746e6.
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One of the fundamental features that separates quantum physics from classical physics is the idea of quantum superposition, also known as coherence. This thesis concentrates on understanding quantum coherence in the mathematical framework of resource theories, viewing it both as a resource to be harnessed and as a way to quantitatively characterise quantum states in contrast to classical states. We first examine the type of coherence resource theory which has emerged recently to cope with general settings where the physical nature of the medium encoding information is not crucial, such as computation. We identify the set of quantum processes in which coherence is neither created nor used, and use these to provide a physically motivated resource theory pictured in terms of interferometry. Using the same concepts, we then find connections between coherence and discord, a type of quantum correlation. In particular, we show how coherence can be used to generate discord, and explore basis-dependent discord as an intermediate quantity. The second part of the thesis applies the resource theory framework to quantify quantum macroscopicity, taken here to mean the extent to which coherence exists in a system on a macroscopic scale. We find the appropriate type of resource theory for this purpose, giving criteria for good measures of macroscopic coherence. We use these criteria to evaluate some previously proposed measures and highlight the role of the quantum Fisher information. Next, we build up measures based on the concept of macroscopic distinguishability and use them to show that macroscopic quantum states are fragile to noise induced by interaction with an environment. Finally, we apply measures based on the Fisher information to a range of experiments involving mechanical degrees of freedom, in order to compare their macroscopicity.
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Adlam, Emily Christine. "Relativistic quantum tasks." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/274930.
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Quantum mechanics, which describes the behaviour of matter and energy on very small scales, is one of the most successful theories in the history of science. Einstein's theory of special relativity, which describes the relationship between space and time, is likewise a highly successful and widely accepted theory. And yet there is a well-documented tension between the two theories, to the extent that it is still not clear that the two can ever be reconciled. This thesis is concerned with furthering the current understanding of the relationship between quantum mechanics and special relativity. In the first part of the thesis we study the behaviour of quantum information in relativistic spacetime. The field of quantum information arose from the realisation that quantum information has a number of crucial properties that distinguish it from classical information, such as the no-cloning property, quantum contextuality, and quantum discord. More recently, it has been realised that placing quantum information under relativistic constraints leads to the emergence of further unique features which are not exhibited by either non-relativistic quantum information or relativistic classical information; as part of this ongoing research programme we develop a new relativistic quantum `paradox' which puts pressure on conventional views about the spatiotemporal persistence of quantum states over time. We then study a new set of relativistic quantum protocols which involve the distribution of entangled states over spacetime, defining one task involving the distribution of the two halves of a known entangled state, and another task involving the distribution of the two halves of an unknown entangled state. The second part of the thesis deals with relativistic quantum cryptography, a field which first began attracting serious attention when it was realised that a cryptographic task known as `bit commitment,' can be implemented with perfect security under relativistic constraints. This result was highly significant, since it is provably impossible to implement bit commitment with perfect security in a purely classical or purely quantum context, and hence bit commitment is an ideal starting point for probing the power of relativistic quantum cryptography. In this thesis we propose several new relativistic quantum bit commitment protocols which have notable advantages over previously known protocols. We then move to a related task, a generalization of zero-knowledge proving which we refer to as knowledge-concealing evidencing of knowledge of a quantum state; we prove no-go theorems concerning the possibility of implementing this task with perfect security, and then set out a relativistic protocol for the task which is asymptotically secure as the dimension of the state in question becomes large. These results have interesting foundational significance above and beyond their applications in the field of cryptography, providing a new perspective on the connections between knowledge, realism and quantum states.
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Cheng, E. L. G. "Higher-dimensional category theory : opetopic foundations." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597569.
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The problem of defining a weak <i>n</i>-category has been approached in various different ways, but so far the relationship between these approaches has not been fully understood. The subject of this thesis is the 'opetopic' theory of <i>n</i>-categories, embracing a group of definitions based on the theory of 'opetopes'. This approach was first proposed by Baez and Dolan, and further approaches to the theory have been proposed by Hermida, Makkai and Power, and Leinster. The opetopic definition of <i>n</i>-category has two stages. First, the language for describing <i>k</i>-cells is set up; this, in the language of Baez and Dolan, is the theory of <i>opetopes. </i>Then, a concept of universality is introduced, to deal with composition and coherence. We first exhibit an equivalence between the three theories of opetopes as far as they have been proposed. We then give an explicit description of the category Opetope of opetopes. We also give an alternative presentation of the construction of opetopes using the 'allowable graphs' of Kelly and MacLane. The underlying data for an opetopic <i>n</i>-category is given by an opetopic set. The category of opetopic sets is described explicitly by Baez and Dolan; we prove that this category is in fact equivalent to the category of presheaves on Opetope. We then turn our attention to the fully definition of (weak) <i>n</i>-categories. We define for each <i>n</i> a category Opic-<i>n</i>-Cat of opetopic <i>n</i>-categories and 'lax <i>n</i>-functors'. We then examine low-dimensional cases, and exhibit an equivalence between the opetopic and classical theories for the cases <i>n</i> £ 2, giving in particular an equivalence between the opetopic and classical approaches to bicategories.
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Maibom, Heidi Lene. "Philosophical foundations of the Theory Theory of folk psychology." Thesis, University College London (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343900.
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Zander, Jascha [Verfasser]. "Squeezed and Entangled Light: From Foundations of Quantum Mechanics to Quantum Sensing / Jascha Zander." Hamburg : Staats- und Universitätsbibliothek Hamburg Carl von Ossietzky, 2021. http://d-nb.info/1240386389/34.
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Oeckl, Robert. "Quantum geometry and Quantum Field Theory." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621912.
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Midgley, Stuart. "Quantum waveguide theory." University of Western Australia. School of Physics, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0036.
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The study of nano-electronic devices is fundamental to the advancement of the semiconductor industry. As electronic devices become increasingly smaller, they will eventually move into a regime where the classical nature of the electrons no longer applies. As the quantum nature of the electrons becomes increasingly important, classical or semiclassical theories and methods will no longer serve their purpose. For example, the simplest non-classical effect that will occur is the tunnelling of electrons through the potential barriers that form wires and transistors. This results in an increase in noise and a reduction in the device?s ability to function correctly. Other quantum effects include coulomb blockade, resonant tunnelling, interference and diffraction, coulomb drag, resonant blockade and the list goes on. This thesis develops both a theoretical model and computational method to allow nanoelectronic devices to be studied in detail. Through the use of computer code and an appropriate model description, potential problems and new novel devices may be identified and studied. The model is as accurate to the physical realisation of the devices as possible to allow direct comparison with experimental outcomes. Using simple geometric shapes of varying potential heights, simple devices are readily accessible: quantum wires; quantum transistors; resonant cavities; and coupled quantum wires. Such devices will form the building blocks of future complex devices and thus need to be fully understood. Results obtained studying the connection of a quantum wire with its surroundings demonstrate non-intuitive behaviour and the importance of device geometry to electrical characteristics. The application of magnetic fields to various nano-devices produced a range of interesting phenomenon with promising novel applications. The magnetic field can be used to alter the phase of the electron, modifying the interaction between the electronic potential and the transport electrons. This thesis studies in detail the Aharonov-Bohm oscillation and impurity characterisation in quantum wires. By studying various devices considerable information can be added to the knowledge base of nano-electronic devices and provide a basis to further research. The computational algorithms developed in this thesis are highly accurate, numerically efficient and unconditionally stable, which can also be used to study many other physical phenomena in the quantum world. As an example, the computational algorithms were applied to positron-hydrogen scattering with the results indicating positronium formation.
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Shin, Ghi Ryang. "Quantum transport theory." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186508.
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Within the framework of the quantum transport theory based on the Wigner transform of the density matrix I study first in non-relativistic and subsequently in relativistic formulation a number of applications. I also develop further the recently proposed relativistic theory: the classical limit is carefully derived and the integral equations of the relativistic Wigner function derived explicitly. I show how it is possible to obtain the Schwinger like particle production rate from relativistic quantum transport equations. Noteworthy numerical results address the shape of the relativistic Wigner function of a given quantum state. Other numerical studies are primarily oriented towards the time evolution of the Wigner function--I can presently solve only the nonrelativistic case in which there is no mixing between particle production and flow phenomena: I consider numerically the fate of the muon after muon catalyzed fusion.
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Schumann, Robert Helmut. "Quantum information theory." Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51892.
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Thesis (MSc)--Stellenbosch University, 2000<br>ENGLISH ABSTRACT: What are the information processing capabilities of physical systems?
As recently as the first half of the 20th century this question did not even have a definite
meaning. What is information, and how would one process it? It took the development of
theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate
mathematically what it means to compute or communicate.
Yet these theories were abstract, based on axiomatic mathematics: what did physical systems
have to do with these axioms? Rolf Landauer had the essential insight - "Information is
physical" - that information is always encoded in the state of a physical system, whose dynamics
on a microscopic level are well-described by quantum physics. This means that we cannot discuss
information without discussing how it is represented, and how nature dictates it should behave.
Wigner considered the situation from another perspective when he wrote about "the unreasonable
effectiveness of mathematics in the natural sciences". Why are the computational techniques
of mathematics so astonishingly useful in describing the physical world [1]? One might begin to
suspect foul play in the universe's operating principles.
Interesting insights into the physics of information accumulated through the 1970s and 1980s
- most sensationally in the proposal for a "quantum computer". If we were to mark a particular
year in which an explosion of interest took place in information physics, that year would have to
be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be
solved easily on a quantum computer. But the applications of information in physics - and vice
versa - have been far more widespread than this popular discovery. These applications range
from improved experimental technology, more sophisticated measurement techniques, methods
for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight
into quantum theory and nature.
In this thesis I present a short review of ideas in quantum information theory. The first chapter
contains introductory material, sketching the central ideas of probability and information theory.
Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with
some useful tools for quantum mechanics of open systems. In the second chapter I outline how
classical information is represented in quantum systems and what this means for agents trying
to extract information from these systems. The final chapter presents a new resource: quantum
information. This resource has some bewildering applications which have been discovered in the
last ten years, and continually presents us with unexpected insights into quantum theory and
the universe.<br>AFRIKAANSE OPSOMMING: Tot watter mate kan fisiese sisteme informasie verwerk?
So onlangs soos die begin van die 20ste eeu was dié vraag nog betekenisloos. Wat is informasie,
en wat bedoel ons as ons dit wil verwerk? Dit was eers met die ontwikkeling van die teorieë van
berekening (in die 1930's) en informasie (in die laat 1940's) dat die tegnologie beskikbaar geword
het wat ons toelaat om wiskundig te formuleer wat dit beteken om te bereken of te kommunikeer.
Hierdie teorieë was egter abstrak en op aksiomatiese wiskunde gegrond - mens sou wel kon
wonder wat fisiese sisteme met hierdie aksiomas te make het. Dit was Rolf Landauer wat uiteindelik
die nodige insig verskaf het - "Informasie is fisies" - informasie word juis altyd in 'n fisiese
toestand gekodeer, en so 'n fisiese toestand word op die mikroskopiese vlak akkuraat deur kwantumfisika
beskryf. Dit beteken dat ons nie informasie kan bespreek sonder om ook na die fisiese
voorstelling te verwys nie, of sonder om in ag te neem nie dat die natuur die gedrag van informasie
voorskryf.
Hierdie situasie is vanaf 'n ander perspektief ook deur Wigner beskou toe hy geskryf het
oor "die onredelike doeltreffendheid van wiskunde in die natuurwetenskappe". Waarom slaag
wiskundige strukture en tegnieke van wiskunde so uitstekend daarin om die fisiese wêreld te
beskryf [1]? Dit laat 'n mens wonder of die beginsels waarvolgens die heelal inmekaar steek
spesiaal so saamgeflans is om ons 'n rat voor die oë te draai.
Die fisika van informasie het in die 1970's en 1980's heelwat interessante insigte opgelewer,
waarvan die mees opspraakwekkende sekerlik die gedagte van 'n kwantumrekenaar is. As ons
één jaar wil uitsonder as die begin van informasiefisika, is dit die jaar 1994 toe Shor ontdek
het dat 'n belangrike probleem van algemene belang (die faktorisering van groot heelgetalle)
moontlik gemaak word deur 'n kwantumrekenaar. Die toepassings van informasie in fisika,
en andersom, strek egter veel wyer as hierdie sleutel toepassing. Ander toepassings strek van
verbeterde eksperimentele metodes, deur gesofistikeerde meetmetodes, metodes vir die ondersoek
en beskrywing van kwantumchaos tot by dieper insig in die samehang van kwantumteorie en die
natuur.
In hierdie tesis bied ek 'n kort oorsig oor die belangrikste idees van kwantuminformasie teorie.
Die eerste hoofstuk bestaan uit inleidende materiaal oor die belangrikste idees van waarskynlikheidsteorie
en klassieke informasie teorie. Kwantummeganika word op 'n gevorderde voorgraadse
vlak ingevoer, saam met die nodige gereedskap van kwantummeganika vir oop stelsels.
In die tweede hoofstuk spreek ek die voorstelling van klassieke informasie en kwantumstelsels
aan, en die gepaardgaande moontlikhede vir 'n agent wat informasie uit sulke stelsels wil kry.
Die laaste hoofstuk ontgin 'n nuwe hulpbron: kwantuminformasie. Gedurende die afgelope tien
jaar het hierdie nuwe hulpbron tot verbysterende nuwe toepassings gelei en ons keer op keer tot
onverwagte nuwe insigte oor kwantumteorie en die heelal gelei.
36
Minto, William Richmond. "Foundations for a realist theory of causality." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ28507.pdf.
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Lockard, Matthew Korthase. "Foundations of epistemic normativity." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1610049891&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Pitalúa-García, Damián. "Quantum information, Bell inequalities and the no-signalling principle." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/245205.
Full textAbstract:
This PhD thesis contains a general introduction and three main chapters. Chapter 2 investigates Bell inequalities that generalize the CHSH and Braunstein-Caves inequalities. Chapter 3 shows a derivation of an upper bound on the success probability of a class of quantum teleportation protocols, denoted as port-based teleportation, from the no-cloning theorem and the no-signalling principle. Chapter 4 introduces the principle of quantum information causality. Chapter 2 considers the predictions of quantum theory and local hidden variable theories (LHVT) for the correlations obtained by measuring a pair of qubits by projections defined by randomly chosen axes separated by a given angle θ. The predictions of LHVT correspond to binary colourings of the Bloch sphere with antipodal points oppositely coloured. We show a Bell inequality for all θ, which generalizes the CHSH and the Braunstein-Caves inequalities in the sense that the measurement choices are not restricted to be in a finite set, but are constrained only by the angle θ. We motivate and explore the hypothesis that for a continuous range of θ > 0, the maximum correlation (anticorrelation) is obtained by assigning to one qubit the colouring with one hemisphere black and the other white, and assigning the same (reverse) colouring to the other qubit. We describe numerical tests that are consistent with this hypothesis and bound the range of θ. Chapter 3 shows a derivation of an upper bound on the success probability of port-based teleportation from the no-cloning theorem and the no-signalling principle. Chapter 4 introduces the principle of quantum information causality, a quantum version of the information causality principle. The quantum information causality principle states the maximum amount of quantum information that a transmitted quantum system can communicate as a function of its dimension, independently of any quantum physical resources previously shared by the communicating parties. These principles reduce to the no-signalling principle if no systems are transmitted. We present a new quantum information task, the quantum information causality game, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combines the quantum teleportation and superdense coding protocols with a task that has classical inputs.
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Bartl, Eduard. "Mathematical foundations of graded knowledge spaces." Diss., Online access via UMI:, 2009.
Find full textAbstract:
Thesis (Ph. D.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Systems Science and Industrial Engineering, 2009.<br>Includes bibliographical references.
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Gupta, Neha. "Homotopy quantum field theory and quantum groups." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/38110/.
Full textAbstract:
The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one (Chapter 3) of the thesis generalises the definition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X-Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice versa. This is the generalisation of the theory given by Turaev into a purely categorical set-up. Part two (Chapter 4) of the thesis generalises the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra in the case of a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the affine case and conjectured for the more general non-affine case. We can construct 3-dimensional HQFTs from modular crossed G-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon (quasitriangular) crossed group-category, and hence can generate 3-dimensional HQFTs under certain conditions if the category becomes modular. However, the problem of systematic finding of modular crossed G-categories is largely open.
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Poletti, Stephen John. "Geometry, quantum field theory and quantum cosmology." Thesis, University of Newcastle Upon Tyne, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315921.
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Kerr, Steven. "Topological quantum field theory and quantum gravity." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/14094/.
Full textAbstract:
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a 1-manifold. The models are independent of the triangulation and give the same result as the continuum partition functions evaluated using zeta-function regularisation. Some implications for more physical models are discussed. In the second part, the gauge gravity action is written using a particularly simple matrix technique. The coupling to scalar, fermion and Yang-Mills fields is reviewed, with some small additions. A sum over histories quantisation of the gauge gravity theory in 2+1 dimensions is then carried out for a particular class of triangulations of the three-sphere. The preliminary stage of the Hamiltonian analysis for the (3+1)-dimensional gauge gravity theory is undertaken.
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Anza, Fabio. "Pure states statistical mechanics : on its foundations and applications to quantum gravity." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:316a0aa7-599d-4831-9d66-160d6c759b72.
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The project concerns the study of the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The goal of this research is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study the equilibrium properties of peculiar quantum systems, which are known to escape thermalization: the many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Then, I exploited the "Concentration of Measure" and the related "Typicality Arguments" to study the macroscopic properties of the basis states in a tentative theory of quantum gravity: Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. The ultimate goal of this line of research is to give a quantum description of a black hole which is consistent with the expected semiclassical behaviour. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why an horizon exhibits thermal properties.
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Davis, Gordon F. "Transcendental arguments and the foundations of ethical theory." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.431048.
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Kim, Steven Hyung. "Mathematical foundations of manufacturing science : theory and implications." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/15283.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, 1985.<br>MICROFICHE COPY AVAILABLE IN ARCHIVES AND DEWEY.<br>Bibliography: leaves 161-167.<br>by Steven Hyung Kim.<br>Ph.D.
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Hamilton, Craig S. "Measurements in quantum theory." Thesis, University of Strathclyde, 2009. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=11885.
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Whitt, Brian. "Gravity : a quantum theory?" Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304522.
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Hele, Timothy John Harvey. "Quantum transition-state theory." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708197.
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Cortese, John A. Preskill John P. "Quantum information theory : classical communication over quantum channels /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-02172004-173217.
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Rogers, Donald J. "Taking theory seriously, pragmatism, truth, and the foundations of international relations theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0004/MQ45118.pdf.
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