Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

This thesis presents a series of studies of thermalization and dissipation in a variety of strongly coupled systems. The main tool for these investigations is the Gauge/Gravity duality, which establishes a correspondence between a d+1-dimensional quantum theory of gravity and a d-dimensional quantum field theory. We study the decay rates of fluctuations around the thermal equilibrium in theories in non-commutative geometry. Rapid thermalization of such fluctuations is found and motivates the conjecture that the phenomena at the black hole horizon is described by non-local physics. In the same type of environment, we analyze the Langevin dynamics of a heavy quark, which undergoes Brownian motion. We find that the late-time behavior of the displacement squared is unaffected by the non-commutativity of the geometry. In a different scenario, we study the correlation functions in theories with quantum critical points. We compute the response of these quantum critical points to a disturbance caused by a massive charged particle and analyze its late time behavior. Finally, we analyze systems far-from-equilibrium as they evolve towards a thermal state. We characterize this evolution for systems with chemical potential by focusing on the ``strong subadditivity" property of their entanglement entropy. This is achieved on the gravity side by using time dependent functions for mass and charge in an AdS-Vaydia metric. / text

The angular momentum of light originates from two sources: one is the spin angular momentum (SAM) of individual photons, which is related to the polarization of light and the other is the orbital angular momentum (OAM) associated with helical wavefront of the light if it is helically phased (complex phase front). A beam of light that is composed of photons possessing both OAM and SAM states can be used in different areas of study such as rotating microscopic particles, interacting with nonlinear materials, investigating atom-light interactions, communication and medical imaging technologies, quantum information, quantum entanglement and etc. In this dissertation we study coherent beams that convey photons in superposition states of polarization and complex phase front. Our study includes two fields: (I) classical wave-like behavior with visible light in the field of singular optics. (II) quantum particle-like behavior of photons of light in the field of quantum-entangled optics. The approach is to investigate the state of such photons both mathematically and experimentally in classical-singular and quantum-entangled fields. We discuss seven projects based on this research. In one project we present a new method to encode OAM modes into perpendicular polarization components and making superpositions of polarization and spatial modes mapped by Poincare sphere. In another project using spatial light modulators (SLM) we realized highorder disclination patterns in the polarization map of the cross section of the beam. We also realize new forms of polarization disclination patterns (line patterns where rotational invariance is violated) known as monstars that were not previously seen. We proposed a new definition for characterizing these patterns since they can have zero or negative singularity index. In another project, instead of SLM we used q-plates to generate new forms of monstars. We proposed a robust and easy method for determining the topological charge of a complex phase front beam by inspecting the interference pattern the beam reflected from a wedged optical flat. In another project we encoded OAM modes onto orthogonal polarization components of a photon from an entangled pair and investigated the quantum entanglement. We also prepared a polarization entangled state and calculated some measures of entanglement. We summarize the projects and discuss the future prospects. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

This dissertation explores two topics located in the intersection of quantum mechanics and cosmology. Entanglement harvesting is a phenomenon in which quantum entanglement can develop between the states of two Unruh-DeWitt detectors travelling through spacetime by way of mutual interaction with a scalar quantum field. I numerically explore entanglement harvesting of Unruh-DeWitt detectors in Minkowski space travelling with constant acceleration, generalizing previous analytical results which held only in a limiting case. Cosmic bubble collisions arise in inflationary cosmology as a mechanism to begin reheating at the end of inflation. I extend the previously proposed theory of boom and bust inflation which relies on the existence of a large extra dimension by exploring particular inflationary models in which reheating need not begin the first time that two bubble walls collide. This allows for a smaller lower bound on the size of the compact extra dimension in the boom and bust proposal.

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Over the past decade, the AdS/CFT correspondence has proven to be a remarkable tool to study various properties of strongly coupled field theories. In the context of the holography, Ryu and Takayanagi have proposed an elegant method to calculate entanglement entropy for these field theories. In this thesis, we use this holographic entanglement entropy to study a candidate c-theorem and entanglement entropy for singular surfaces. We use holographic entanglement entropy for strip geometry and construct a candidate c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a ‘phase transition’ as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop. Then, we turn towards studying the holographic entanglement entropy for regions with a singular boundary in higher dimensions. Here, we find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge c. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, extended singularities contribute through new linear or quadratic terms in logarithm only when the locus of the singularity is even dimensional and curved.

Quantum computing resources have been known to provide speed-ups in computational complexity in many algorithms. The impact of these resources in communication, however, has not attracted much attention. We investigate the impact of quantum entanglement on communication complexity. We provide a positive result, by presenting a class of multi-party communication problems wherein the presence of a suitable quantum entanglement lowers the classical communication complexity. We show that, in evaluating certains function whose parameters are distributed among various parties, the presence of prior entanglement can help in reducing the required communication. We also present an outline of realizing the required entanglement through optical photon quantum computing. We also suggest the possible impact of our results on network information flow problems, by showing an instance of a lower bound which can be broken by adding limited power to the communication model.

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There are various notions of positivity for matrices and linear matrix-valued maps that play important roles in quantum information theory. The cones of positive semidefinite matrices and completely positive linear maps, which represent quantum states and quantum channels respectively, are the most ubiquitous positive cones. There are also many natural cones that can been regarded as "more" or "less" positive than these standard examples. In particular, entanglement theory deals with the cones of separable operators and entanglement witnesses, which satisfy very strong and weak positivity properties respectively. Rather complementary to the various cones that arise in entanglement theory are norms. The trace norm (or operator norm, depending on context) for operators and the diamond norm (or completely bounded norm) for superoperators are the typical norms that are seen throughout quantum information theory. In this work our main goal is to develop a family of norms that play a role analogous to the cone of entanglement witnesses. We investigate the basic mathematical properties of these norms, including their relationships with other well-known norms, their isometry groups, and their dual norms. We also make the place of these norms in entanglement theory rigorous by showing that entanglement witnesses arise from minimal operator systems, and analogously our norms arise from minimal operator spaces. Finally, we connect the various cones and norms considered here to several seemingly unrelated problems from other areas. We characterize the problem of whether or not non-positive partial transpose bound entangled states exist in terms of one of our norms, and provide evidence in favour of their existence. We also characterize the minimum gate fidelity of a quantum channel, the maximum output purity and its completely bounded counterpart, and the geometric measure of entanglement in terms of these norms. / Natural Sciences and Engineering Research Council (Canada Graduate Scholarship), Brock Scholarship