In this work we mainly focus on two main aspects of interest within the field of Relativistic Quantum Information. We first expand on the current knowledge of the effects of relativity on entanglement between global field modes. Within this aspect, we focus on two topics: we address and revise the single mode approximation commonly used in the literature. We study the nonlocal correlations of charged bosonic field modes and the degradation of entanglement initially present in maximally entangled states as a function of acceleration, when one observer is accelerated. In the second part of this work we introduce, develop and exploit a method for confining quantum fields within one (or two) cavities and analyzing the effects of motion of one cavity on the entanglement initially present between cavity field modes. One cavity is always allowed to undergo arbitrary trajectories composed of segments of inertial motion and uniform acceleration. We investigate how entanglement is degraded, conserved and created as a function of the parameters describing the motion and we provide the analytical tools to understand how these effects occur. We conclude this work by analyzing the effects of the change of spatial topology on the nonlocal correlations present in the Hawking-Unruh radiation in the topological geon analogue of black hole spacetimes.
In this work we mainly focus on two main aspects of interest within the field of Relativistic Quantum Information. We first expand on the current knowledge of the effects of relativity on entanglement between global field modes. Within this aspect, we focus on two topics: we address and revise the single mode approximation commonly used in the literature. We study the nonlocal correlations of charged bosonic field modes and the degradation of entanglement initially present in maximally entangled states as a function of acceleration, when one observer is accelerated. In the second part of this work we introduce, develop and exploit a method for confining quantum fields within one (or two) cavities and analyzing the effects of motion of one cavity on the entanglement initially present between cavity field modes. One cavity is always allowed to undergo arbitrary trajectories composed of segments of inertial motion and uniform acceleration. We investigate how entanglement is degraded, conserved and created as a function of the parameters describing the motion and we provide the analytical tools to understand how these effects occur. We conclude this work by analyzing the effects of the change of spatial topology on the nonlocal correlations present in the Hawking-Unruh radiation in the topological geon analogue of black hole spacetimes.
A central aim of relativistic quantum information (RQI) is the investigation of quantum information tasks and resources taking into account the relativistic aspects of nature. More precisely, it is of fundamental interest to understand how the storage, manipulation, and transmission of information utilizing quantum systems are influenced by the fact that these processes take place in a relativistic spacetime. In particular, many studies in RQI have been focused on the effects of non-uniform motion on entanglement, the main resource of quantum information protocols. Early investigations in this direction were performed in highly idealized settings that prompted questions as to the practical accessibility of these results. To overcome these limitations it is necessary to consider quantum systems that are in principle accessible to localized observers. In this thesis we present such a model, the rigid relativistic cavity, and its extensions, focusing on the effects of motion on entanglement and applications such as quantum teleportation. We study cavities in (1+1) dimensions undergoing non-uniform motion, consisting of segments of uniform acceleration and inertial motion of arbitrary duration that allow the involved velocities to become relativistic. The transitions between segments can be sharp or smooth and higher dimensions can be incorporated. The primary focus lies in the Bogoliubov transformations of the quantum fields, real scalar fields or Dirac fields, confined to the cavities. The Bogoliubov transformations change the particle content and the occupation of the energy levels of the cavity. We show how these effects generate entanglement between the modes of the quantum fields inside a single cavity for various initial states. The entanglement between several cavities, on the other hand, is degraded by the non-uniform motion, influencing the fidelity of tasks such as teleportation.
Quantum effects in accelerated frames and gravitational fields have been studied for decades. One of the most influential outcomes is the discovery of thermal radiation from a black hole by Hawking in 1975. Other important discoveries include the Unruh effect, dynamical Casimir effect etc.. Although these discoveries are very exciting, experimental verification of them is extremely challenging. Even in the theoretical aspect, not all the issues have been resolved, e.g., the well known black hole information paradox. Quantum information science was developed rapidly during the last thirty years. The well established concepts and tools in quantum information science have been used to explore the quantum effects in gravitational fields and relativistic frames, giving birth to a new research field named relativistic quantum information. This thesis studies quantum effects in accelerated frames and gravitational fields by exploiting the concepts and techniques in quantum information science. The Unruh effect implies that the state of the fields confined within part of the Minkowski spacetime can appear thermal, and entanglement exists between different spacetime regions. We show that the particle number distribution of the field modes confined within a finite diamond region is also thermal in the Minkowski vacuum, an analogue to the Unruh effect; and there exists entanglement between different diamonds. The vacuum entanglement can be extracted and utilized for some quantum information protocols, e.g., quantum key distribution. Furthermore, we show that the presence of a horizon and the Unruh thermal noise has important consequences to the quantum communication protocols where one of the parties is a uniformly accelerated observer. Interactions between uniformly accelerated objects and quantum fields are traditionally studied using perturbation theory. The quantum circuit model, a crucial tool in quantum communication and computation, can be exploited to calculate radiations from the uniformly accelerated objects non-perturbatively. By further combining field detection scheme in quantum optics, e.g., homodyne detection, the output field from the uniformly accelerated objects can be fully studied. These techniques help to study decoherence effect in non-inertial frames, which may provide important insights for the black hole information paradox. Dynamical spacetimes generally create quantum particles. Gravitational perturbations around a black hole oscillate and decay, due to the emission of gravitational waves to spatial infinity and into the black hole. We show that they play the role as a multimode squeezer, squeezing the state of the quantum fields and creating particles.
In this thesis we shall apply techniques from quantum information theory to the problem of measuring the structure of spacetime or equivalently measuring the gravitational field. In turn we will also look at how acceleration may effect quantum information techniques for processing and transmitting information. Measuring the structure of spacetime is a slight abuse of terminology as spacetime structure is not directly observable. We will be investigating the estimation of spacetime structure by making measurements on quantum systems which depend on the spacetime background. The structure of spacetime and the gravitational field will be treated in accordance with Einstein's general theory of relativity. This is currently the most accurately tested classical theory for gravity. It is widely believed that fundamentally, gravity should be treated within the framework of quantum mechanics, just like the other forces of nature. This is yet to be seen experimentally and a theory capable of falsifiable predictions is yet to be found. In this thesis we shall focus on the effects of gravity at the classical level, however we shall treat matter and non-gravitational energy using quantum mechanics. When looking at how gravity effects quantum information we will specifically be focusing on the simple case of acceleration, yet we shall treat it in this relativistic spacetime context. Knowing the structure of spacetime in general relativity amounts to knowing an object called the metric tensor. This object contains all the information about a spacetime. This may include local curvature, for instance around a star or black hole, gravitational radiation coming from a binary pulsar and even the large scale structure of the universe such as the rate of expansion. By performing local experiments one may attempt to extract this information. Fundamentally these experiments will be governed by quantum mechanics, hence the accuracy of the estimation will be fundamentally limited by the statistical nature of quantum theory. In this thesis we shall develop an equation which states just what accuracy one can ultimately achieve when attempting to measure the structure of spacetime. This equation will be shown to be a generalisation of known results for the accuracy to which one can ultimately measure position and momentum as well as time and energy. The result will be applied to a range of relativistic phenomena including acceleration in flat spacetime, the local curvature around a black hole, the amplitude of a gravitational wave and the expansion of the universe in a cosmological model. Following the use of quantum information theory to investigate gravity we shall look at how acceleration can effect quantum information. Firstly we shall see how quantum entanglement can be created and stored between two optical cavities when one is uniformly accelerating. This is in contrast to a number of results which predict that entanglement will be lost in the presence of acceleration. This loss of entanglement is predicted due to an as yet unobserved phenomena known as the Unruh effect. The Unruh effect states that an observer uniformly accelerating will see a thermal distribution of particles even if an inertial observer will see no particles at all. We will show how the use of optical cavities can prevent this effect from causing problems both for the storage and creation of entanglement. Finally we shall look at how a particular quantum detection scheme can be employed in the presence of acceleration. Our technique will emphasis the importance of locality, that is the localisation of physics in spacetime. We will also show how some commonly used approximations used to study the Unruh effect, can be avoided with our new formulation.
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from special relativity, quantum optics, general relativity, quantum communication and quantum computation. The high level of current interest in these subjects is exemplified by the recent award of the 2012 Nobel Prize in Physics to Serge Haroche and David J Wineland for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems. It is our hope that this issue will encourage new researchers to enter this rapidly developing and exciting new field. R B Mann and T C Ralph Guest Editors
This thesis collects my own and collaborative work I have been involved with finding localised systems in quantum field theory that are useful for quantum information. It draws from many well established physical theories such as quantum field theory in curved spacetimes, quantum optics and Gaussian state quantum information. The results are split between three chapters. For the first results, we set-up the basic framework for working with quantum fields confined to cavities. By considering the real Klein-Gordon field, we describe how to model the non-uniform motion of a rigid cavity through spacetime. We employ the use of Bogoliubov transformations to describe the effects of changing acceleration. The second set of results investigate how the Dirac field can be confined to a cavity for quantum information purposes. By again considering Bogoliubov transformations, we thoroughly investigate how the entanglement shared between two cavities is affected by non-uniform motion. It is shown that different types of Dirac field states are more robust against motion than others. The final results look at using our second notion of localisation, Unruh- DeWitt detectors. We investigate how allowing for a "non-point-like" spatial profile of the Unruh-DeWitt detector affects how it interacts with a quantum field around it. By engineering suitable detector-field interactions, we use techniques from symplectic geometry to compute the dynamics of a quantum state beyond commonly used perturbation theory. There is also a conclusions chapter at the end of the thesis which summarises the results presented and suggestions of possible new directions of research in relativistic quantum information are made.
An open question in the field of relativistic quantum information is how parties in arbitrary motion may distribute and store quantum entanglement. We propose a scheme for storing quantum information in the field modes of cavities moving in flat space-time and analyze it in a quantum field theoretical framework. In contrast with previous work that found entanglement degradation between observers moving with uniform acceleration, we find the quantum information in such systems is protected. We further discuss a method for establishing the entanglement in the first place and show that in principle it is always possible to produce maximally entangled states between the cavities.