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Wei, Tzu-Chieh 2012-11-11T16:42:50Z 2012-11-11T16:42:50Z 10000-01-01 2004 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. Submitted by Elias Lopez (erlopez2@illinois.edu) on 2012-11-11T16:42:50Z No. of bitstreams: 1 Wei_Tzu-Chieh.pdf: 1464082 bytes, checksum: 816a10cb2b7b481ed3a046fbde193027 (MD5) Made available in DSpace on 2012-11-11T16:42:50Z (GMT). No. of bitstreams: 1 Wei_Tzu-Chieh.pdf: 1464082 bytes, checksum: 816a10cb2b7b481ed3a046fbde193027 (MD5) Previous issue date: 2004 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elias Lopez (erlopez2@illinois.edu) on 2012-11-14T01:50:19Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:11:40-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Publisher has not yet granted open access permission Publisher has not yet granted open access permission U of I Only http://hdl.handle.net/2142/35200 en 2004 © Quantum; Multi-Partite; two-qubit; isotropic; entanglement; hartee; entrope; distillation; werner Quantum Entanglement: Geometric Quantification and Applications to Multi-partite States and Quantum Phase Transitions Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.