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Separable States Are More Disordered Globally than Locally

Nielsen, M. A. and Kempe, J. (2001) Separable States Are More Disordered Globally than Locally. Physical Review Letters, 86 (22). pp. 5184-5187. ISSN 0031-9007. doi:10.1103/PhysRevLett.86.5184.

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A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice ( A) and Bob ( B), may be more disordered locally than globally. That is, S(A)>S(A,B), where S(̇) is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is nonseparable. In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone. This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions.

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Additional Information:©2001 The American Physical Society Received 29 November 2000 We thank Carl Caves and Pranaw Rungta for discussions about separability and quantum information in general. J. K. thanks the Centre for Quantum Computer Technology at the University of Queensland for its hospitality and acknowledges support by the U.S. ARO under Contract/Grant No. DAAG55-98-1-0371.
Issue or Number:22
Record Number:CaltechAUTHORS:NIEprl01
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1966
Deposited By: Archive Administrator
Deposited On:27 Feb 2006
Last Modified:08 Nov 2021 19:44

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