My dissertation consists of two independent parts. Part one of my dissertation examines concepts of quantum information. I clarify three very different concepts of information and assess their implications for understanding quantum mechanics. First I clarify the concept of information due to Shannon, and its relation to physical theories. Using the Shannon concept, I examine two purportedly new concepts of quantum information. I argue that a fundamental philosophical mistake is made regarding these concepts. Advocates of these new concepts do not properly distinguish between the properties of information due to the physical medium it is stored in from the properties of information per se. This distinction is crucial for developing a new concept to help us understand quantum mechanics and evaluating its merits. Part two of my dissertation examines explanations of the efficiency that quantum computers enjoy over classical computers for some computational tasks, and the relationship between explanations of efficiency and interpretations of quantum mechanics. I examine the so-called quantum parallelism thesis, that quantum computers can perform many computations in a single step, a feat thought not to be possible on classical computers. The truth of this thesis is not obvious, and contested by some. I develop a set of general criteria for computation that any computing device must satisfy. I use these criteria to demonstrate that the quantum parallelism thesis is true. As an application of these general criteria for computation I articulate three distinct concepts of parallelism and demonstrate that classical computers can compute in parallel as well. This demonstrates that the truth of the quantum parallelism thesis alone does not provide a complete explanation of the efficiency of quantum computers. I supplement the quantum parallelism thesis to provide a complete explanation. Finally, I address the claim that only the many-worlds interpretation of quantum mechanics can underwrite the truth of the quantum parallelism thesis. The general criteria for computation provide support for the quantum parallelism thesis independent of any interpretation of quantum mechanics.
My dissertation consists of two independent parts. Part one of my dissertation examines concepts of quantum information. I clarify three very different concepts of information and assess their implications for understanding quantum mechanics. First I clarify the concept of information due to Shannon, and its relation to physical theories. Using the Shannon concept, I examine two purportedly new concepts of quantum information. I argue that a fundamental philosophical mistake is made regarding these concepts. Advocates of these new concepts do not properly distinguish between the properties of information due to the physical medium it is stored in from the properties of information per se. This distinction is crucial for developing a new concept to help us understand quantum mechanics and evaluating its merits. Part two of my dissertation examines explanations of the efficiency that quantum computers enjoy over classical computers for some computational tasks, and the relationship between explanations of efficiency and interpretations of quantum mechanics. I examine the so-called quantum parallelism thesis, that quantum computers can perform many computations in a single step, a feat thought not to be possible on classical computers. The truth of this thesis is not obvious, and contested by some. I develop a set of general criteria for computation that any computing device must satisfy. I use these criteria to demonstrate that the quantum parallelism thesis is true. As an application of these general criteria for computation I articulate three distinct concepts of parallelism and demonstrate that classical computers can compute in parallel as well. This demonstrates that the truth of the quantum parallelism thesis alone does not provide a complete explanation of the efficiency of quantum computers. I supplement the quantum parallelism thesis to provide a complete explanation. Finally, I address the claim that only the many-worlds interpretation of quantum mechanics can underwrite the truth of the quantum parallelism thesis. The general criteria for computation provide support for the quantum parallelism thesis independent of any interpretation of quantum mechanics.
The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches - that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism - fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel conceptual framework from which to conduct this analysis.
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.
Computation and quantum information [1] are an extension of the information process concept, and they are used for the effects of quantum mechanic [2]. This new scheme provides a work scene that is not restricted to only two operations; on the contrary, this can gain multiple intermediate states as a result of these two ways of superposition. By performing this operation, the system can evaluate all possibilities in only one step by making a parallel computation; meanwhile, in the classic way, this evaluation is carried out independently of each other, and in different steps. The quantum parallelism can be defined as a reduction in time and an increase in the fast of information process. In this chapter, the fundamental elements that make possible to use the mechanical-quantum phenomena as a tool in the process information are presented.
The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit a tentative resolution to it. In particular, I argue that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always be representable as product states. Chapter 2 begins with a discussion of the most popular of the candidate physical explanations for quantum speedup: the many worlds explanation. I argue that unlike the neo-Everettian interpretation of quantum mechanics it does not have the conceptual resources required to overcome the `preferred basis objection'. I further argue that the many worlds explanation, at best, can serve as a good description of the physical process which takes place in so-called network-based computation, but that it is incompatible with other models of computation such as cluster state quantum computing. I next consider, in Chapter 3, a common component of most other candidate explanations of quantum speedup: quantum entanglement. I investigate whether entanglement can be said to be a necessary component of any explanation for quantum speedup, and I consider two major purported counter-examples to this claim. I argue that neither of these, in fact, show that entanglement is unnecessary for speedup, and that, on the contrary, we should conclude that it is. In Chapters 4 and 5 I then ask whether entanglement can be said to be sufficient as well. In Chapter 4 I argue that despite a result that seems to indicate the contrary, entanglement, considered as a resource, can be seen as sufficient to enable quantum speedup. Finally, in Chapter 5 I argue that entanglement is sufficient to explain quantum speedup as well.
Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum theory has changed in an equally dramatic manner our understanding of information processing and computation. On one hand, the fundamental properties of quantum systems can be harnessed to transmit, store, and manipulate information in a more efficient and secure way than possible in the realm of classical physics. On the other hand, the development of systematic procedures to manipulate systems of a large number of particles in the quantum regime, crucial to the implementation of quantum-based information processing, has triggered new possibilities in the exploration of quantum many-body physics and related areas. In this thesis, we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement, intrinsically quantum correlations, and the exploration of the use of controlled quantum systems to the computation and simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement
This thesis is a study of how information theory can be used to analyse and interpret quantum mechanical systems, specifically, systems that are being used for information processing and communication tasks. Quantum information science is a relatively new field, and it has only been recently that we have started to look at using quantum mechanical systems to accomplish information processing tasks that are not possible using classical systems. As this method of information processing is a relatively new paradigm, there are many possibilities for new algorithms and discoveries in this area of computing. The application of information theory towards the analysis and description of quantum mechanical systems yields new interesting results - it can even be argued that information theory provides a natural and intuitive way to intepret quantum mechanics, as correlations and measurement outcomes in quantum processes can be described using information theory. Chapter 1 is an introduction to the strange new world of quantum mechanics and takes a brief look at one of the applications of quantum information science in quantum cryptography. A mathematical overview of the postulates and framework that quantum mechanics is built on is presented in Chapter 2. Chapter 3 is a brief study of classical information theory and some of the fundamental concepts and ideas that form the crux of the subject. In Chapter 4, we present the main results of the thesis by taking a look at an optimal measurement scheme that improves on previous schemes by allowing us to extract the maximal amount of information from states in a quantum channel of specific geometry. The findings have an impact on various other areas of the field, including security analysis of quantum cryptographic protocols and building better quantum cloning machines.