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.
The treatment is pedagogical and suitable for beginning graduates in the field.
Book chapter in "Thermodynamics in the quantum regime - Recent Progress and Outlook" -- This chapter is a survey of the published literature on quantum batteries -- ensembles of non-degenerate quantum systems on which energy can be deposited, and from which work can be extracted. A pedagogical approach is used to familiarize the reader with the main results obtained in this field, starting from simple examples and proceeding with in-depth analysis. An outlook for the field and future developments are discussed at the end of the chapter.
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter 4 studies the problem of quantum parameter estimation and introduces the quantum particle filter as a practical computational method for parameter estimation via continuous measurement. Chapter 5 applies these techniques in magnetometry and studies the estimator's uncertainty scalings in a double-pass atomic magnetometer. Chapter 6 presents an efficient fee…
In this thesis we study continuously observed open quantum systems from the point of view of quantum filtering theory. The conditioned state of the open system obeys a non-commutative or quantum analogue of the Kushner-Stratonovich equation in classical filtering theory. The thesis consists out of four chapters. The first chapter is a brief introduction to quantum probability theory and quantum stochastic calculus. The second chapter is a description of a photon counting experiment in continuous time within the framework of Davies and Srinivas. The third chapter focusses on the derivation of t…
This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information science. Our results of the analysis of certain quantum information protocols using this optimization technique are presented, and an implementation of a relevant numerical tool is introduced. The key method used is NPA discovered by Navascues et al. [Phys. Rev. Lett. 98, 010401 (2007)]. In chapter 1 a brief overview of mathematical methods used in this work is presented. In chapter 2 an introduction to quantum information science is given. Chapter 3 concerns the dev…
The main focus of this thesis is to study the nonclassical and phase properties of a family of engineered quantum states, most of which show various nonclassical features. The beauty of these states is that these states can be used to establish quantum supremacy. Earlier, a considerable amount of works has been reported on various types of quantum states and their nonclassical properties. Here, complementing the earlier works, the effect of non-Gaussianity inducing operators on the nonclassical and phase properties of displaced Fock states have been studied. This thesis includes 6 chapters. In…
This dissertation treats the topics of threshold calculation, ancilla construction, and non-standard error models. Chapter 2 introduces background material ranging from quantum mechanics to classical coding to thresholds for quantum computation. In Chapter 3 numerical and analytical means are used to generate estimates of and bounds on the threshold given an error model described by a restricted stochastic Pauli channel. Chapter 4 develops a simple, flexible means of estimating the threshold and applies it to some cases of interest. Finally, a novel method of ancilla construction is proposed i…
The subject of this thesis are various properties of quantum states that make them "non-classical" and their behaviour under unitary operations. In chapter 2 some basic concepts of quantum mechanics and quantum information are reviewed. In chapter 3 properties of quantum states analysed in the literature are identified. I chapter 4 relations between them are analysed: whether possessing of one property by a given state implies possessing another property by the same state. In chapter 5 the central notion of the thesis is introduced, namely possessing a given property in absolute vs. non-absolu…
In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the control fields are characterized as well as their isolation from their environment. In chapter 2, I review some background material on open-loop quantum control theory. Chapter 3 provides a derivation of the Hamiltonians arising from electromagnetic fields that we use to control our alkali atomic spins. In chapter 4, I develop an algorithm for state preparation,…
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Grössing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely …
The work is devoted to the investigation of the influence of a heat bath on the physical processes in a quantum system. We use the density matrix theory as one of the most powerfool tool for investigation of quantum relaxation. In the beginning of the work (chapter 2) we mention and recall the most important steps of derivation of the equation of motion for the reduced density matrix (master equation) for an arbitrary quantum system in diabatic representation interacting with the environment modeled by a set of independent harmonic oscillators. Chapter 3 deals with the question of the border b…
This chapter describes the application of lasers, specifically diode lasers, in the area of quantum key distribution (QKD). First, we motivate the distribution of cryptographic keys based on quantum physical properties of light, give a brief introduction to QKD assuming the reader has no or very little knowledge about cryptography, and briefly present the state-of-the-art of QKD. In the second half of the chapter we describe, as an example of a real-world QKD system, the system deployed between the University of Calgary and SAIT Polytechnic. We conclude the chapter with a brief discussion of q…
We provide ways to turn ancillas into phase gates (chapter 1), leading to irrational phase gates (chapter 2). We realize all the 2-qubit permutation gates (chapter 3).
Quantum technologies are enjoying an unprecedented popularity, and some applications are already in the market. This thesis studies two phenomena that are behind a lot of quantum technologies: entanglement and nonlocality. We focus on multipartite systems, and ask what configurations of those systems are more useful than others. 'Usefulness' takes on different meanings depending on the context, but, roughly speaking, we aim for more entanglement or more nonlocality. Chapter 2 develops a resource theory of entanglement with a unique multipartite maximally entangled state. Chapter 3 shows that a…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also we describe the general concepts of the two-particle scattering problem as a tool to construct Jastrow terms in trial wave functions. Chapter 2 explains in details the Quantum Monte Carlo methods employed in our calculations from the theoretical and practical points of view. In Chapter 3 we explain the Ewald summation technique, applied to a power-law 1/|r|k…
This thesis presents a wide-ranging study of localising relational degrees of freedom. Three physical systems are studied in depth, each built upon a simple measurement-based process. For each physical system - light from independent sources leaking onto a beam splitter monitored by photodetectors, spatially interfering Bose-Einstein condensates extracted from separate preparation procedures, and delocalised massive particles or mirrors scattering light which is detected in the far-field - the thesis investigates the key features of the underlying process of localisation, and explores the prop…
In this PhD thesis, several aspects regarding maximal entanglement are analyzed. In the first chapter, Bell Inequalities are analyzed from an operational perspective as well as novel Bell inequalities are obtained together with their optimal settings for a maximal violation. Multipartite figures of merit, in particular, the hyperdeterminant, are the subject of the second chapter. They are applied to detect quantum phase transitions in several spin models. The third chapter focuses on the simulation of the XY model in a quantum computer. The quantum circuit obtained is tested in three current q…
The work that we present in this thesis tries to be at the crossover of quantum information science, quantum many-body physics, and quantum field theory. We use tools from these three fields to analyze problems that arise in the interdisciplinary intersection. More concretely, in Chapter 1 we consider the irreversibility of renormalization group flows from a quantum information perspective by using majorization theory and conformal field theory. In Chapter 2 we compute the entanglement of a single copy of a bipartite quantum system for a variety of models by using techniques from conformal fie…
The framework of this thesis is fault-tolerant quantum algorithms. Grover's algorithm and quantum walks are described in Chapter 2. We start by highlighting the central role that rotations play in quantum algorithms, explaining Grover's, why it is optimal, and how it may be extended. Key subroutines explained in this area are amplitude amplification and quantum walks, which will constitute useful parts of other algorithms. In the third chapter, in contrast, we turn to the exponential advantages promised by the Fourier transform in the context of the hidden subgroup problem. However, since this…
In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints. The focus of our research is on the gapped many-body quantum systems including symmetry-protected topological states and topologically ordered states. Chapter 1. Introduction. Chapter 2. Geometric phase, wavefunction overlap, spacetime path integral and topological invariants. Chapter 3. Aspects of Symmetry. Chapter 4. Aspects of Topology. Chapter 5. Aspects of Anomalies. Chapter 6. Quantum Statistics and Spacetime Surgery.…
The present thesis shows that Quantum Information concepts can be used to better understand the quantum-to-classical boundary in mesoscopic and macroscopic systems. Our findings suggest a way to push this boundary towards the macroscopic domain by coupling a moveable mirror to a confined quasi-classical electromagnetic field (Chapters 2 and 3), and opens new possibilities towards quantum computation and information processing with strongly-correlated systems at realistic temperatures by demonstrating the opening of robust gaps in 2D antiferromagnetic lattices due to the presence of additional …
The technologies utilizing quantum states of light have been in the spotlight for the last two decades. In this regard, quantum metrology, quantum imaging, quantum-optical communication are some of the important applications that exploit fascinating quantum properties like quantum superposition, quantum correlations, and nonclassical photon statistics. However, the state-of-art technologies operating at the single-photon level are not robust enough to truly realize a reliable quantum-photonic technology. In Chapter 1, I present a historical account of photon-based technologies. Furthermore, I …
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is the quantum separability problem. Chapters 1 to 3 motivate a new interior-point algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. When all the expected values are known, the algorithm solves the sepa…
This is a chapter on quantum cryptography for the book "A Multidisciplinary Introduction to Information Security" to be published by CRC Press in 2011/2012. The chapter aims to introduce the topic to undergraduate-level and continuing-education students specializing in information and communication technology.
This document explores how to make music using quantum computing algorithms. The text is an unedited pre-publication chapter which will appear in the book "Quantum Computer Music", Miranda, E. R. (Editor). This chapters provides the background and specific details of a collaboration formed in 2021 between the Quantum Engineering Technology Labs - a quantum computing and technology research group at the University of Bristol - and music artist, producer and audio engineer Simon Small. The goal of the collaboration was to explore how the data and concepts used in the research at the university c…
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
In this job, we will present a theory called Quantum Tomography that is the natural extension of the theory of detection of signals in classical telecommunications to Quantum Mechanics. This theory mainly consists in the reconstruction of a quantum state of a system through a probability distribution measured directly in the laboratory, usually called Tomogram. This Thesis contains five chapters. In the first one, we will show the birth of this theory as an adaptation of homodyne and heterodyne classical detection to Quantum Mechanics. In the second, we will describe a tomographic description …
The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in thermodynamics, the platform of quantum-thermal machines sheds light on thermodynamics in the quantum regime. This chapter focuses on the basic features of quantum mechanics, such as energy quantization, the uncertainty principle, quantum coherence and correlations, and their manifestation in microscopic thermal devices. In addition to indicating the peculiar behaviors o…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly in a variational approach. In the first Chapter we introduce the subject in the broader context of many-body quantum mechanics, and briefly sketch the history of the field. The second Chapter tries to summarise what is known about N-representability of reduced density matrices, and derives these results in a unified framework. The optimisation problem can be…
This dissertation is dedicated to investigating quantum optical effects involving single photons in tailored structures. It consists of six chapters and an appendix. The central part of the thesis starts with a chapter titled "Theoretical background" where the author introduces key quantum optical concepts needed for understanding the subsequent chapters. The next chapter is devoted to a discussion of the estimation of the Sellmeier coefficient in nonlinear crystals with the SPDC process. The accuracy and feasibility of the method are analysed in the context of the experimental results. The su…
Broadly speaking, this thesis is about nonlinear optics, quantum mechanics, and computing. More specifically, it covers four main topics: Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO Dynamics. Tying them all together is a theory of open quantum systems called the SLH model, which I introduce in Chapters 1-2. The SLH model is a general framework for open quantum systems that interact through bosonic fields, and is the basis for the quantum circuit theory developed in the text. Coherent LQG control is discussed in Chapters 3-4, where I demonstrate that c…
The complex electronic structure and unusual potential energy curve of the chromium dimer have fascinated scientists for decades, with agreement between theory and experiment so far elusive. Here, we present a new ab initio simulation of the potential energy curve and vibrational spectrum that significantly improves on all earlier estimates. Our data support a shift in earlier experimental assignments of a cluster of vibrational frequencies by one quantum number. The new vibrational assignment yields an experimentally derived potential energy curve in quantitative agreement with theory across …
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse …
PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review chapters on entanglement and distillation.
In this PhD thesis, we will present the theoretical and experimental work that led to the realization of a radio-frequency circuit quantum electrodynamics system (RFcQED). In chapter 2, we provide a detailed derivation of the Hamiltonian of circuit QED formulated in the context of the Rabi model, and extract expressions for the cross-Kerr interaction. The resulting requirements for the coupling rate in RFcQED are discussed, one of them being the need to dramatically increase the coupling rate compared to typical circuit QED device. In chapter 3 we cover two experimental approaches to increasin…
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 …
With the emergence of quantum computers, a new field of algorithmic music composition has been initiated. The vast majority of previous work focuses on music generation using gate-based quantum computers. An alternative model of computation is adiabatic quantum computing (AQC), and a heuristic algorithm known as quantum annealing running in the framework of AQC is a promising method for solving optimization problems. In this chapter, we lay the groundwork of music composition using quantum annealing. We approach the process of music composition as an optimization problem. We describe the funda…
This book provides an introduction to the emerging field of quantum thermodynamics, with particular focus on its relation to quantum information and its implications for quantum computers and next generation quantum technologies. The text, aimed at graduate level physics students with a working knowledge of quantum mechanics and statistical physics, provides a brief overview of the development of classical thermodynamics and its quantum formulation in Chapter 1. Chapter 2 then explores typical thermodynamic settings, such as cycles and work extraction protocols, when the working material is ge…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical formulation of both can be expressed in terms of unital C*-algebras, in which case it becomes clear that they have the same general structure, with quantum mechanics a noncommutative generalization of the classical case. In purely mathematical terms it is seen that quantum mechanics is a noncommutative generalization of probability theory. The most important insight i…
The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a ma…
The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same input-output process compare to each other? In the proposed framework, an input-output process is modelled by a causally structured channel in some fixed theory, and its implementations are modelled by causally structured dilations formalising hidden side-computations. These dilations compare through a pre-order formalising relative strength of side-computation…
In this chapter a quantum communication protocol with use of repeaters is presented. The protocol is constructed for qudits i.e. the generalized quantum information units. One-dit teleportation is based on the generalized Pauli-Z (phase-flip) gate's correction. This approach avoids using Pauli-X and Hadamard gates unlike in other known protocols based on quantum repeaters which were constructed for qubits and qudits. It is also important to mention that the repeaters based on teleportation protocol, described in this chapter, allow a measurement in the standard base (what simplifies the measur…
We suppose that a structure working as a quantum switch will be a significant element of future networks realizing transmissions of quantum information. In this chapter we analyze a process of switch's operating -- especially in systems with a noise presence. The noise is caused by a phenomenon of quantum decoherence, i.e. distorting of quantum states because of an environmental influence, and also by some imperfections of quantum gates' implementation. In the face of mentioned problems, the possibility of tracing the switch's behavior during its operating seems very important. To realize that…
[Shortened Abstract:] This thesis explores the possibility that quantum probabilities arose thermodynamically. A chief concern is the detection of primordial `quantum nonequilibrium', since this is observably distinct from textbook quantum physics. Chapters 2, 3, 4, and 5 are adaptations of references [1,2,3], and [4] respectively. Chapter 2 proposes (information) entropy conservation as a minimal requirement for a theory to feature classical-style thermodynamic relaxation. The resulting structure is dubbed `the iRelax framework'. Both classical mechanics and de Broglie-Bohm quantum theory are…
This chapter covers recent developments in the field of hybrid quantum photonics based on color centers in nanodiamonds and Si3N4-photonics towards a technology platform with applications in quantum information processing and quantum information distribution. The methodological approach can be divided in three main tasks. First, the fabrication and optimization of Si3N4-photonics. Second, the creation, characterization and control of color centers in nanodiamonds. Third, the assembly of hybrid quantum photonics by integrating the nanodiamonds into the photonic structures. One focus will be the…
This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can be exhibited not only at the level of their static version, but also at the level of their dynamical version. We present a combined analysis of these systems, employing tools of random matrix theory and stochastic calculus as well as tools of quantum mechanics, in order to solve some original problems. Further from the detailed presentation of the field and t…
Already in the first edition of this book (Barone and Paterno, "Fundamentals and Physics and Applications of the Josephson Effect", Wiley 1982), a great number of interesting and important applications for Josephson junctions were discussed. In the decades that have passed since then, several new applications have emerged. This chapter treats one such new class of applications: quantum optics and quantum information processing (QIP) based on superconducting circuits with Josephson junctions. In this chapter, we aim to explain the basics of superconducting quantum circuits with Josephson juncti…
