Lorenza Viola and Winton G Brown 2007 J. Phys. A: Math. Theor. 40 8109 doi:10.1088/1751-8113/40/28/S17
Generalized entanglement as a framework for complex quantum systems: purity versus delocalization measures
Lorenza Viola and Winton G Brown
Show affiliationsWe establish contact between the delocalization properties of pure quantum states, as quantified by their number of principal components, and the average generalized entanglement properties, as quantified by purity measures relative to different observable sets. We find that correlations between products of state vector components with respect to Hamming distance play an important role in the structure of subsystem-based purity measures. In particular, we derive general conditions under which the amount of global multipartite entanglement relates to the inverse participation ratio averaged over a maximal set of mutually unbiased product bases. Furthermore, we provide a method for computing the expected amount of generalized entanglement with respect to an arbitrary observable set for random pure states. Specific examples and an explicit application to a disordered quantum spin chain are discussed.
- PACS
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03.67.Lx Quantum computation architectures and implementations
03.67.Mn Entanglement measures, witnesses, and other characterizations
- MSC
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81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 28 (13 July 2007)
Received 30 October 2006, in final form 12 January 2007
Published 27 June 2007
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Generalized entanglement as a framework for complex quantum systems: purity versus delocalization measures
Lorenza Viola and Winton G Brown 2007 J. Phys. A: Math. Theor. 40 8109
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