Quantum Entanglement: Geometric Quantification and Applications to Multi-partite States and Quantum Phase Transitions
Wei, Tzu-Chieh
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https://hdl.handle.net/2142/35200
Description
Title
Quantum Entanglement: Geometric Quantification and Applications to Multi-partite States and Quantum Phase Transitions
Author(s)
Wei, Tzu-Chieh
Issue Date
2004
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Quantum; Multi-Partite; two-qubit; isotropic; entanglement; hartee; entrope; distillation; werner
Language
en
Abstract
The degree to which a pure quantum state is entangled can be characterized by the distance
or angle to the nearest unentangled state. This geometric measure of entanglement is explored
for bi-partite and multi-partite pure and mixed states. It is determined analytically for arbitrary two-qubit mixed states, generalized Werner, and isotropic states, and is also applied to certain multi-partite mixed states, including two distinct multi-partite bound entangled states. Moreover, the ground-state entanglement of the XY model in a transverse field is calculated and shown to exhibit singular behavior near the quantum critical line. Along the way, connections are pointed out between the geometric measure of entanglement, the Hartree approximation, entanglement witnesses, correlation functions, and the relative entropy of entanglement.
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