Quantum Entanglement: Geometric Quantification and Applications to Multi-partite States and Quantum Phase Transitions

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Wei, Tzu-Chieh

• Quantum; Multi-Partite; two-qubit; isotropic; entanglement; hartee; entrope; distillation; werner

Statement dc:rights

• 2004 ©

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/35200

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/35200