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.

In this thesis, we develop a number of operational tests and tools for benchmarking the quantum nature of optical quantum communication devices. Using the laws of quantum physics, ideal quantum devices can fundamentally outperform their classical counterparts, or even achieve objectives which are classically impossible. Actual devices will not be ideal, but they may still be capable of facilitating quantum communication. Benchmarking tests, based on the presence of entanglement, can be used to verify whether or not imperfect quantum devices offer any advantage over their classical analogs. The general goal in this thesis is to provide strong benchmarking tools which simultaneously require minimal experimental resources but also offer a wide range of applicability. Another major component is the extension of existing qualitative benchmarks (`Is it quantum or classical?') to more quantitative forms (`How quantum is it?'). We provide a number of benchmarking results applicable to two main situations, namely discrete remote state preparation protocols and continuous-variable quantum device testing. The theoretical tools derived throughout this thesis are also applied to the tasks of certifying a remote state preparation experiment and a continuous-variable quantum memory.

Quantum information and quantum computation are linked by a common mathematical and physical framework of quantum mechanics. The manipulation of the predicted dynamics and its optimization is known as quantum control. Many techniques, originating in the study of nuclear magnetic resonance, have found common usage in methods for processing quantum information and steering physical systems into desired states. This thesis expands on these techniques, with careful attention to the regime where competing effects in the dynamics are present, and no semi-classical picture exists where one effect dominates over the others. That is, the transition between the diabatic and adiabatic error regimes is examined, with the use of such techniques as time-dependent diagonalization, interaction frames, average-Hamiltonian expansion, and numerical optimization with multiple time-dependences. The results are applied specifically to superconducting systems, but are general and improve on existing methods with regard to selectivity and crosstalk problems, filtering of modulation of resonance between qubits, leakage to non-compuational states, multi-photon virtual transitions, and the strong driving limit.

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.

Over the last few decades, quantised excitations of the electromagnetic field have proven to be an ideal system with which to investigate and harness quantum optical phenomena. The techniques developed have enabled fundamental tests of quantum mechanics as well as practical applications in quantum metrology and quantum information processing. Advancing to larger-scale entangled quantum systems will open up new regimes of quantum many-body physics, allowing us to probe the limits of quantum mechanics and enabling truly quantum-enhanced technologies. However, moving towards this goal will require further experimental and theoretical innovations. The work described in this thesis focuses on several different aspects of optical quantum information, but are ultimately all linked by this long-term aim. The first part of this thesis describes a novel method for strain-based active control of quantum optical circuits and a new method for the characterisation of high efficiency detectors. Building on this, I discuss in detail two different fields of quantum optics that stand to benefit from these techniques. I initially consider quantum-enhanced metrology, including work aimed towards demonstrating a truly better-than-classical phase measurement, and a theoretical exploration of multiple-phase estimation. Finally, I focus on linear-optical quantum information processing, exploring in detail the use of time-frequency encodings for quantum computing.

We look at the problem of verifying optical entanglement for two types of states relevant to quantum information processing. One type occurs in Hong-Ou-Mandel interference and is relevant to quantum computing. The other type is time frequency entanglement which is useful for quantum key distribution. For these types of states the conventional methods of entanglement verification do not work well, and we develop new criteria and methods to verify entanglement of such states. Explicitly, one method takes into account the possible multimode character of two photons, while the other method takes into account the missing data that occur due to the finite range of detectors. This dissertation includes previously published and unpublished co-authored material.

The Theory of Games is a mathematical formalism used to analyze conflicts between two or more parts. In those conflicts, each part has a group of actions (strategies) that aids them in the optimization of their objectives. The objectives of the players are the rewards (payoffs) given according to their chosen strategy. By quantizing a game, advantages in operational efficiency and in the stability of the game solutions are demonstrated. In a quantum game, the strategies are operators that act on an isolated system. A natural issue is to consider a game in an open system. In this case the strategies are changed by Kraus operators which represent a natural measurement of the environment. We want to find the necessary physical conditions to model a quantum open system as a game. To analyze this issue we applied the formalism of Quantum Operations on the Fröhlich system and we described it as a model of Quantum Game. The interpretation is a conflict among different configurations of the environment which, by inserting noise in the main system exhibits regimes of minimum loss of information. On the other hand, the model of Fröhlich has been used to describe the biophysical dynamics of the neuronal microtubules. By describing the model of Fröhlich in the Quantum Game formalism, we have shown that regimes of stability may exist even under physiological conditions. From the evolutionary point of view, the Theory of Games can be the key to describe the natural optimization at sub-neuronal levels. / A Teoria de Jogos (TJs) é um formalismo matemático usado para analisar situações de conflitos entre duas ou mais partes. Nesses conflitos, cada parte possui um conjunto de ações (estratégias) que auxilia na otimização de seus objetivos. Os objetivos dos jogadres são as recompensas (payoffs) que cada um recebe de acordo com a estratégia adotada. Ao se quantizar um jogo, mostra-se ganhos em eficiência operacional e ganhos na estabilidade das soluções. Em um jogo quântico (JQ), as estratégias são operadores que atuam num sistema isolado. Uma questão natural é considerar um jogo num sistema aberto. Nesta situação as estratégias são trocadas por operadores de Kraus que representam uma medida natural do ambiente. Nosso interesse é encontrar as condições físicas necessáriaas para modelarmos um sistema quântico aberto como um jogo. Para analisar essa questão aplicamos o formalismo de Operações Quânticas (OQs) sobre o sistema de Fröhlich e o apresentamos como um modelo de JQ. A interpretação é um conflito entre diferentes configurações do ambiente que, ao inserirem ruído no sistema principal, exibem regiões de mínima perda de informação. O modelo de Fröhlich vem sendo usado para descrever a dinâmica biofísica dos microtúbulos neuronais. Ao estruturamos o modelo de Fröhlich nos JQs, mostramos que as regiões de estabilidade podem existir sob condições fisiológicas. Usando o aspecto evolucionista, a TJs pode ser a chave para a descrição de processos de otimização da informação em nível sub-neuronal.

The no-cloning theorem is one of the fundamental concepts of quantum information theory. It tells us that no general quantum state can be perfectly replicated. In this thesis we introduce the notion of imperfect cloning, and define the properties of the universal cloning machine. Furthermore, we construct an ansatz of how our universal cloning machine should perform as to produce two imperfect clones from one input qubit. We find an optimal fidelity of 5/6 for our universal cloning machine. We then reevaluate our ansatz and construct a class of unitary transformations such that an optimal fidelity is always achieved. Lastly, we present an overview of some applications of imperfect quantum cloning in the field of quantum information.

Neste trabalho estudamos as propriedades de emaranhamento dos estados de dois quasifótons de frequências diferentes, fazendo a aproximação de que o vácuo de quasifótons é igual ao vácuo de fótons, no caso em que não temos campo externo algum e no caso da presença de um campo magnético externo, constante e homogêneo. Estudamos também as propriedades de emaranhamento do próprio vácuo de quasifótons e dos estados de dois quasifótons no caso monocromático, sem campo externo e com o vácuo de quasifótons levado em conta exatamente. / In this work we study the properties of entanglement of the states of two quasi-photons of different frequencies, considering the approximation that the quasi-photon\'s vacuum is equal the photon\'s vacuum, in the case where we have no external field and in the case where we have an external, constant and homogeneous magnetic field. We study also the properties of entanglement of the quasi-photon\'s vacuum and of the states of two quasi-photons in the monochromatic case, without external field and with the quasi-photon\'s vacuum considered exactly.

O papel das medidas de complexidade tem se tornado cada vez mais claro na extensão da compreensão que se tem sobre sistemas complexos. Todavia, apesar do grande número de medidas propostas para capturar tais características em sistemas clássicos, para sistemas quânticos somente vê-se extensões da complexidade algorítmica de Kolmogorov. Assim, propõe-se neste trabalho a extensão de três medidas de complexidade pelo uso do ferramental da teoria da informação quântica para torná-las capazes de compreender a quantificação da complexidade de estados quânticos. Resultados mostram que alguns fenômenos observados em sistemas complexos clássicos estão presentes em estados bipartite e tripartite de qubits e estão intimamente ligados com a presença de entrelaçamento nos mesmos. Tanto comprovação de conceitos já conhecidos como indícios de novos fenômenos foram observados, ambos com possíveis aplicações tecnológicas. / The role of complexity measures has become increasingly clear on the extent of understanding we have of complex systems. However, despite the large number of measures proposed to capture these characteristics in classical systems, to quantum systems there are only extensions of the Kolmogorov\'s algorithmic complexity. Thus, this work proposes the extension of three measures of complexity by using the tools of quantum information theory to make them able to understand the quantification of the complexity of quantum states. Results show that some phenomena observed in classical complex systems are present in bipartite and tripartite states of qubits and are closely linked with the presence of entanglement in them. Both proof of known concepts as signs of new phenomena were observed, with possible technological applications.