In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tends to zero. We investigate the observers' abilities to precisely measure the parameter of a state that is communicated between Alice and Rob. This parameter was encoded to either the amplitudes of a single excitation state or the phase of a NOON state. With NOON states the dual rail encoding provided greater precision, which is different to the results for the other situations. The precision was maximum for a particular number of excitations in the NOON state. We calculated the bipartite communication for Alice-Rob and Alice-AntiRob beyond the single mode approximation. Rob and AntiRob are causally disconnected counter-accelerating observers. We found that Alice must choose in advance with whom, Rob or AntiRob she wants to create entanglement using a particular setup. She could communicate classically to both.
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tends to zero. We investigate the observers' abilities to precisely measure the parameter of a state that is communicated between Alice and Rob. This parameter was encoded to either the amplitudes of a single excitation state or the phase of a NOON state. With NOON states the dual rail encoding provided greater precision, which is different to the results for the other situations. The precision was maximum for a particular number of excitations in the NOON state. We calculated the bipartite communication for Alice-Rob and Alice-AntiRob beyond the single mode approximation. Rob and AntiRob are causally disconnected counter-accelerating observers. We found that Alice must choose in advance with whom, Rob or AntiRob she wants to create entanglement using a particular setup. She could communicate classically to both.
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.
Quantum information investigates the possibility of enhancing our ability to process and transmit information by directly exploiting quantum mechanical laws. When searching for improvement opportunities, one typically starts by assessing the range of outcomes classically attainable, and then investigates to what extent control over the quantum features of the system could be helpful, as well as the best performance that could be achieved. In this thesis we provide examples of these aspects, in linear optics, quantum metrology, and quantum communication. We start by providing a criterion able to certify whether the outcome of a linear optical evolution cannot be explained by the classical wave-like theory of light. We do so by identifying a tight lower bound on the amount of correlations that could be detected among output intensities, when classical electrodynamics theory is used to describe the fields. Rather than simply detecting nonclassicality, we then focus on its quantification. In particular, we consider the characterisation of the amount of squeezing encoded on selected quantum probes by an unknown external device, without prior information on the direction of application. We identify the single-mode Gaussian probes leading to the largest average precision in noiseless and noisy conditions, and discuss the advantages arising from the use of correlated two-mode probes. Finally, we improve current bounds on the ultimate performance attainable in a quantum communication scenario. Specifically, we bound the number of maximally entangled qubits, or private bits, shared by two parties after a communication protocol over a quantum network, without restrictions on their classical communication. As in previous investigations, our approach is based on the evaluation of the maximum amount of entanglement that could be generated by the channels in the network, but it includes the possibility of changing entanglement measure on a channel-by-channel basis. Examples where this is advantageous are discussed.
The Hawking effect is an exciting physical prediction lying at the intersection of the two most successful theories of the past century, namely, Einstein’s theory of relativity and quantum mechanics. In this dissertation, we put special emphasis on the quantum aspects of the Hawking process encoded in the entanglement shared by the emitted fluxes of created quanta. In particular, we employ sharp tools from quantum information theory to quantify the entanglement produced by the Hawking effect throughout the black hole evaporation process. Our framework allows us to extend previous calculations of entanglement to a larger set of cases, for instance, the situation where a black hole is immersed in a thermal bath, such as the cosmic microwave background (CMB), and the quantum state of infalling radiation is, therefore, mixed. Motivated by recent intense experimental efforts, we extend our framework to the case of an optical white-black hole pair analog gravity system created by a strong electromagnetic pulse propagating in a non-linear dielectric medium. One of the main results presented in this dissertation is the development of a numerical code that recreates the Hawking process in such an optical analog. Utilizing this code together with our quantum information tools, we study how different input quantum states of light alter the amount of the entanglement produced in the Hawking pairs. We find that although ambient thermal noise and detector inefficiencies, unsurprisingly, tend to reduce quantum correlations in the Hawking process, when horizons are illuminated with single-mode squeezed states of light, the entanglement generated increases in a tunable manner. As a last application in optical analogs, we investigate the laser configuration in which two strong electromagnetic pulses propagate in a non-linear dielectric medium exchanging Hawking quanta, thus, stimulating each other. In such a setup, we observe that not only the number of Hawking quanta created is exponentially increased but also the entanglement shared between the mode of the electromagnetic field inside the laser cavity with the modes of the field outside the cavity grows with time. We conclude that these novel results open a promising window for the observability of the quantum origin of the Hawking effect in the lab.
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.
We study the effect of the acceleration of the observer on a parameter estimation protocol using NOON states. An inertial observer, Alice, prepares a NOON state in Unruh modes of the quantum field, and sends it to an accelerated observer, Rob. We calculate the quantum Fisher information of the state received by Rob. We find the counterintuitive result that the single-rail encoding outperforms the dual rail. The NOON states have an optimal N for the maximum information extractable by Rob, given his acceleration. This optimal N decreases with increasing acceleration.
Recently, there has been increased interest in understanding entanglement and quantum communication in black hole spacetimes and in using quantum information techniques to address questions in gravity. Studies on relativistic entanglement show the emergence of conceptually important qualitative differences to a non-relativistic treatment. For instance, entanglement was found to be an observer-dependent property that changes from the perspective of accelerated observers moving in flat spacetime. Relativisitic quantum information theory uses well-known tools coming from quantum information and quantum optics to study quantum effects provoked by gravity to learn information about the spacetime. We can take advantage of our knowledge about quantum correlations and effects produced by the gravitational interaction to set the basis for experimental proposals ultimately aiming at finding corrections due to quantum gravity effects, too mild to be directly observed. This doctoral thesis dissertation summarises most of the research carried out during my PhD on this topic.