We study the entanglement of two-qubit systems resulting from local interactions with spatially extended bosonic systems. Our results apply to the case where the initial state of the bosonic system is represented by a statistical mixture of states with fixed particle number. In particular, we derive and discuss necessary conditions to generate entanglement in the two-qubit system. We also study the scenario where the joint system is initially in its ground state and the interaction is switched on adiabatically. Using time independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theory

Thesis (Ph.D.)--Boston University / Quantum entanglement and non-locality are non-classical characteristics of quantum states with phase coherence that are of central importance to physics, and relevant to the foundations of quantum mechanics and quantum information science. This thesis examines quantum entanglement and non-locality in two- and three-component quantum states with phase coherence when they are subject to statistically independent, classical, Markovian, phase noise in various combinations at the local and collective level. Because this noise reduces phase coherence, it can also reduce quantum entanglement and Bell non-locality. After introducing and contextualizing the research, the results are presented in three broad areas. The first area characterizes the relative time scales of decoherence and disentanglement in 2 x 2 and 3 x 3 quantum states, as well as the various subsystems of the two classes of entangled tripartite two-level quantum states. In all cases, it was found that disentanglement time scales are less than or equal to decoherence time scales. The second area examines the finite-time loss of entanglement, even as quantum state coherence is lost only asymptotically in time due to local dephasing noise, a phenomenon entitled "Entanglement Sudden Death" (ESD). Extending the initial discovery in the simplest 2 x 2 case, ESD is shown to exist in all other systems where mixed-state entanglement measures exist, the 2 x 3 and d x d systems, for finite d > 2. The third area concerns non-locality, which is a physical phenomenon independent of quantum mechanics and related to, though fundamentally different from, entanglement. Non-locality, as quantified by classes of Bell inequalities, is shown to be lost in finite time, even when decoherence occurs only asymptotically. This phenomenon was named "Bell Non-locality Sudden Death" (BNSD).

In the 1990¡¦s, the research of quantum information attracts many people¡¦s attention. In this period of time, Shor find a new method to demonstrate that a quantum computer could factor very large numbers super-efficiently. The method also shows that quantum computer has more potential than classical computer. Beside, quantum information contains many different new fields, such as quantum computation, quantum entanglement, quantum searching, etc. We believe the most fundamental physics of the applications of quantum information is quantum entanglement. In order to understand the physical meaning of entanglement, we choose entanglement as the goal of our thesis.

Quantum theories have had an unprecedented success in providing a framework for studying physical systems. A fundamental implication of these theories is the existence of so-called entangled states, that is states whose description cannot be reduced to their constituents. These states are purely quantum and there is no such analogue in classical physics, where knowing the state of every particle is sufficient to infer the state of the system they compose. Entanglement is a core element of many quantum algorithms, quantum teleportation, quantum communications and quantum cryptographic scenarios. Furthermore, entanglement is present in nearly all solid-state systems, when they are at, or close to, their state of lowest energy. Therefore, it is both a technological resource and also a property which needs to be investigated in order to achieve understanding of real world materials at a fundamental level. The most concise demonstration of entanglement is perhaps in the case of maximal entanglement between two spin-l/2 particles. These maximally entangled two- particle states are called Bell states and they have been used to demonstrate experimentally that quantum mechanics is inequivalent to classical mechanics. A gen- eralization of this setting comes from studying entanglement between two physical systems, these can be either pure or mixed (e.g. in contact with a thermal bath). Entanglement between two systems, also knows as bipartite entanglement, has been studied in depth and quantified through various measures. However bipartite entanglement, by definition, is not the only quantity of in- terest. In some cases, entanglement is global and its properties cannot be reduced to studying bi-partitions. This type of entanglement, so-called multipartite entanglement, is harder to quantify and to study in general. Its presence is profound in physical systems that are at the point of undergoing a quantum phase transition and it is also a core ingredient for quantum error correcting codes, performing classical computation with quantum resources and some cryptographic scenarios. In this thesis we study properties of systems with multi-partite entanglement in the context of renormalization and quantum phase transitions, we show that multi- partite entanglement can be used to perform cryptographic tasks and we investigate what classes of Hamiltonians generate multiartite entanglement, while at the same time, their action can be simulated efficiently by a classical computer.

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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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