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The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes

Source: J. Math. Phys. 50, 122104 (2010); doi:10.1063/1.3271041

Published 28 December 2009

KEYWORDS and PACS
Keywords
PACS
  • 03.65.Ud
    Entanglement and quantum nonlocality
  • 03.67.Mn
    Entanglement measures, witnesses, and other characterizations (quantum information)
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • YEAR: 2010
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PUBLICATION DATA
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Masahito Hayashi,1 Damian Markham,2 Mio Murao,3,4 Masaki Owari,5 and Shashank Virmani5,6
1Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan
2LTCI CNRS, TELECOM ParisTech, 37/39 rue Dareau, 75014 Paris, France
3Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
4Institute for Nano Quantum Information Electronics, The University of Tokyo, Tokyo 113-0033, Japan
5Optics Section, Blackett Laboratory and Institute for Mathematical Sciences, Imperial College, London SW7 2AZ, United Kingdom
6Department Physics, SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
In this paper for a class of symmetric multiparty pure states, we consider a conjecture related to the geometric measure of entanglement: “for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a symmetric product state.” We show that this conjecture is true for symmetric pure states whose amplitudes are all non-negative in a computational basis. The more general conjecture is still open. ©2009 American Institute of Physics
History: Received 20 June 2009; accepted 10 November 2009; published 28 December 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/122104/1

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