Quantum effects in non-inertial frames and curved space-time have been studied for decades. One of the most intriguing discoveries is the existence of virtual particles in the quantum vacuum. One example in which such particles can be observed is through the Unruh effect, which predicts that a uniformly accelerated observer would see a thermal bath of (virtual) particles in the quantum vacuum. Initial doubts on the existence of these virtual particles were allayed by the Unruh De-Witt (UDW) detector, which promoted these virtual particles to real excitations of the detector. Ever since, semiclassical approaches to relativistic quantum field theory (QFT) in flat and curved space-time have been predominantly analysed through a two-level Unruh De-Witt detector utilizing perturbation theory. It is noted, however, that the change of relativistic frame preserves Gaussian properties (e.g. Gaussian distribution of the Wigner function) of the system. In this thesis, we specifically explore the effects of relativistic (non-inertial) reference frames on QFT by considering relativistic QFT in flat-space time. These systems are analysed from the perspective of Gaussian quantum information, via homodyne detection and UDW detectors with a harmonic oscillator degree of freedom.Our project starts by reviewing and developing bipartite/multi-partite entanglement measures (specifically, entanglement of formation), in the hope that we can utilize these measures to understand the entanglement properties of the quantum vacuum. In general, these measure have infinite degrees of freedom and are incomputable. In this project the multi-partite entanglement measure is applied to the Gaussian regime, which reduces the number of degrees of freedom to a finite one, hence making it a computable measure.In our next project, we attempt to understand how relativistic reference frames affect the communication between different observers. To obtain an intuition of its effect, a passive (time-delay) signal sent from a uniformly accelerated observer to a stationary observer was analysed. When we naively implemented the self-homodyne detection scheme, the signal appeared noisy. This effect was referred to as apparent decoherence, and its effect could be traced back to our naive assumption that all of the signal’s information would be stored in the time-delayed mode; the vacuum entanglement that pre-existed before the (time-delay) signal was created must be accounted for. We follow by analysing the effects that emerge due to communication between different relativistic reference frames. We then develop a communication technique referred to as ideal-homodyne which is a homodyne detection scheme robust to these effects. We used this detection scheme to analyse the correlation/entanglement properties of an accelerated signal (created via accelerated mirror, squeezer and phase shifter) sent to an inertial observer.In our last project, we utilize the knowledge that was gained through the prior projects to analyse (subcycle) electro-optic sampling. In the literature, there were doubts as to whether electro-optic sampling were truly detecting virtual particles in the quantum vacuum, or particle excitations that were created as a by-product of the detection mechanism. We were able to pin-point some similarities between electro-optic sampling and subcycle probe via the UDW detector. The regime in which the electro-optic sampling directly maps virtual particles from the vacuum into real excitations of the probe field was identified by establishing an equivalence to the UDW detector in certain parameter regimes.
Quantum effects in non-inertial frames and curved space-time have been studied for decades. One of the most intriguing discoveries is the existence of virtual particles in the quantum vacuum. One example in which such particles can be observed is through the Unruh effect, which predicts that a uniformly accelerated observer would see a thermal bath of (virtual) particles in the quantum vacuum. Initial doubts on the existence of these virtual particles were allayed by the Unruh De-Witt (UDW) detector, which promoted these virtual particles to real excitations of the detector. Ever since, semiclassical approaches to relativistic quantum field theory (QFT) in flat and curved space-time have been predominantly analysed through a two-level Unruh De-Witt detector utilizing perturbation theory. It is noted, however, that the change of relativistic frame preserves Gaussian properties (e.g. Gaussian distribution of the Wigner function) of the system. In this thesis, we specifically explore the effects of relativistic (non-inertial) reference frames on QFT by considering relativistic QFT in flat-space time. These systems are analysed from the perspective of Gaussian quantum information, via homodyne detection and UDW detectors with a harmonic oscillator degree of freedom.Our project starts by reviewing and developing bipartite/multi-partite entanglement measures (specifically, entanglement of formation), in the hope that we can utilize these measures to understand the entanglement properties of the quantum vacuum. In general, these measure have infinite degrees of freedom and are incomputable. In this project the multi-partite entanglement measure is applied to the Gaussian regime, which reduces the number of degrees of freedom to a finite one, hence making it a computable measure.In our next project, we attempt to understand how relativistic reference frames affect the communication between different observers. To obtain an intuition of its effect, a passive (time-delay) signal sent from a uniformly accelerated observer to a stationary observer was analysed. When we naively implemented the self-homodyne detection scheme, the signal appeared noisy. This effect was referred to as apparent decoherence, and its effect could be traced back to our naive assumption that all of the signal’s information would be stored in the time-delayed mode; the vacuum entanglement that pre-existed before the (time-delay) signal was created must be accounted for. We follow by analysing the effects that emerge due to communication between different relativistic reference frames. We then develop a communication technique referred to as ideal-homodyne which is a homodyne detection scheme robust to these effects. We used this detection scheme to analyse the correlation/entanglement properties of an accelerated signal (created via accelerated mirror, squeezer and phase shifter) sent to an inertial observer.In our last project, we utilize the knowledge that was gained through the prior projects to analyse (subcycle) electro-optic sampling. In the literature, there were doubts as to whether electro-optic sampling were truly detecting virtual particles in the quantum vacuum, or particle excitations that were created as a by-product of the detection mechanism. We were able to pin-point some similarities between electro-optic sampling and subcycle probe via the UDW detector. The regime in which the electro-optic sampling directly maps virtual particles from the vacuum into real excitations of the probe field was identified by establishing an equivalence to the UDW detector in certain parameter regimes.
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 examine a variety of question regarding several quantum information-theoretic concepts as they manifest in the context of relativistic quantum fields. In particular, we study the qualitative and quantitative structure of entanglement (as well as more generalized quantum correlations) in field theory. Primarily we study the nature of vacuum entanglement, but consider spatial correlations in more general field states as well. We also discuss several novel aspects of particle creation phenomena, which generally go hand in hand with the presence of field entanglement. Such investigations are important from two perspectives. First, we gain enlightening new insight into the nature of quantum fields and, therefore, into the fundamental constituents of the matter contained in our universe. Second, we are able to consider the possibility of utilizing the relativistic nature of quantum fields as a resource for quantum technological tasks such as entanglement distribution, information processing, and metrology. \n \nAs a general guiding principle, here we approach such questions from an operational perspective. That is, we focus less on the mathematical facts derivable from a given theory and instead attempt to answer in what concretely physical ways such facts manifest themselves. For example, in what ways can vacuum entanglement actually be experimentally detected and measured, at least in principle? Such an approach allows us to circumvent otherwise problematic interpretational issues. It also lends itself more naturally to the proposal of real world experiments regarding, and utilizations of, the physics being investigated. In this thesis we utilize two models of detection as applied to field theory. \n \nThe first is one that we will develop from scratch and use to great effect in a number of studies; this is the non-perturbative oscillator detector. In this context, a ``detector" is simply some quantum system that is allowed to interact in some way with a quantum field. The response of this system then gives us information about the field properties. Typically such studies are done perturbatively, which presents several severe limitations on what may be investigated. We develop an alternative model, in which the detector is identified as a quantum harmonic oscillator, that allows non-perturbative solutions. We go on to apply this model to a variety of studies. We start by the examining the Unruh effect in a cavity setting. Not only are we able to examine the thermalization behavior of such a detector (which is stronger than what can be achieved perturbatively), we also demonstrate that the Unruh response is largely independent of the cavity boundary conditions, indicating a surprising amount of generality and universality to the phenomenon. We also consider the spacelike extraction of spatial entanglement by a set of such detectors. This includes the harvesting of genuine tripartite entanglement out of the vacuum, as well as the observation that the extractable quantum discord (a generalized measure of quantum correlations) can be greatly amplified by thermal fluctuations in the field, in opposite behavior to entanglement. This calls into question the nature of quantum discord, but also suggests at the possibility of actually using environmental noise as a quantum computational resource. Next, we use the oscillator detector model to great effect by proposing a method of reliably and sustainably generating and distributing entanglement via a cavity field. This protocol is inherently non-perturbative, and we refer to it as entanglement farming. Lastly, we modify the farming scenario to discover a very sensitive resonance effect that generates a large difference in the protocol output due to a minute change in system parameters, including the length of cavity being used. We put this forth as a potential method of quantum seismic metrology. \n \nThe second model that we will consider simply involves performing projective measurements onto a given set of field modes. We will find, however, that such an approach allows us to solve previously intractable problems. In particular, we apply this procedure to the physically sensible choice of localized, positive frequency field modes. Using this model we perform two different studies. In the first, we consider the response of an observer accelerating not through the vacuum state but rather a thermal state. Such a setting has not been (properly) studied previously, due to the computational challenges involved. By applying the localized projective measurement model we are able determine that such an observer sees both an Unruh response from acceleration and a response from the field thermality and that, critically, these responses are distinguishable. We then go on to examine the degradation of quantum correlations between two observers due to the acceleration of one of the observers. This is a prototypical scenario of interest and, by applying realistic measurement assumptions, we obtain results qualitatively different from many previous works on the issue. \n \nIn addition to these models, we question the nature of vacuum entanglement and particle creation by considering an operationally straightforward procedure that greatly demystifies these phenomena and puts them on to solid, physically concrete grounds. This operation is that of very quickly introducing a boundary condition onto one's field, for example by creating a mirror. The real particles generated in this process will then be quantum entangled with each other, even if they are created at spatially separate locations, and this entanglement derives exactly from the previously present vacuum entanglement. Not only does this realization provide an operationally satisfying interpretation of vacuum entanglement, it also suggests a straightforward procedure for its experimental verification. \n \nIn all of this, the computational framework that we will rely upon is that of Gaussian quantum mechanics. This is a restriction of continuous variable quantum mechanics that, while limited in its applicability, provides extremely powerful computational tools in the cases that it may be used. The scenarios of interest in this thesis fall within this category and lend themselves naturally to a Gaussian approach. With this we are able to perform, near trivially, many otherwise intractable studies.
This thesis considers entanglement, an important resource for quantum information processing tasks, while taking into account the theory of relativity. Not only is this a more complete description of quantum information, but it is necessary to fully understand quantum information processing tasks done by systems in arbitrary motion. \n \nIt is shown that accelerated measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The entanglement produced increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration. \n \nThe dynamics of entanglement between two Unruh-DeWitt detectors, one stationary and the other undergoing non-uniform acceleration, was studied numerically. In the ultraweak coupling limit, the entanglement decreases as a function of time for the parameters considered and decreases faster than if the moving detector had had a uniform acceleration.
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.
In this thesis we focus on the influence of uniform acceleration on quantum states and their properties, as well as on quantum entanglement contained in the vacuum. First, we analyze a quantum clock measuring time in terms of the decay of an unstable particle. We compare the rate of ticking of a stationary clock to the one of a uniformly accelerating clock. We discover that there exists a deviation from what the discrepancy between those rates is predicted to be by special relativity. In a further part of this thesis we focus on the family of two-mode Gaussian states of two localized modes of a given quantum field. A general framework is developed for investigating the properties of such states, when observed by two uniformly accelerated observers, having access to another pair of localized modes. In particular, we focus on the vacuum state and examine the amount of quantum entanglement perceived by the observers. The framework is developed for three cases: the quantum scalar field in 1+1 and 3+1 dimensions and the Dirac spinor field in 1+1 dimensions. We find that in general more entanglement is seen when the accelerations of the observers increase and when the size of the modes of the observers and their central frequencies decrease. Furthermore, we extend our attention also to tripartite entanglement and investigate its extraction from the quantum vacuum by three particle detectors in a cavity, interacting with a quantum field for a finite time. Detailed maps of amounts of tripartite and bipartite entanglement extracted by the detectors, are produced and compared between two types of boundary conditions. It is found vacuum entanglement is most easily extracted in the case of periodic boundary conditions and it is easier to extract tripartite than bipartite entanglement.
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.