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

Abstract

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.

Authors:
 [1];  [2];  [3];  [4];  [4]
  1. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579 (Japan)
  2. LTCI CNRS, TELECOM ParisTech, 37/39 rue Dareau, 75014 Paris (France)
  3. Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan)
  4. Optics Section, Blackett Laboratory and Institute for Mathematical Sciences, Imperial College, London SW7 2AZ (United Kingdom)
Publication Date:
OSTI Identifier:
21294514
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 50; Journal Issue: 12; Other Information: DOI: 10.1063/1.3271041; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GEOMETRY; HILBERT SPACE; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; SYMMETRY

Citation Formats

Hayashi, Masahito, Markham, Damian, Murao, Mio, Institute for Nano Quantum Information Electronics, University of Tokyo, Tokyo 113-0033, Owari, Masaki, Virmani, Shashank, and Department Physics, SUPA, University of Strathclyde, Glasgow G4 0NG. The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes. United States: N. p., 2009. Web. doi:10.1063/1.3271041.
Hayashi, Masahito, Markham, Damian, Murao, Mio, Institute for Nano Quantum Information Electronics, University of Tokyo, Tokyo 113-0033, Owari, Masaki, Virmani, Shashank, & Department Physics, SUPA, University of Strathclyde, Glasgow G4 0NG. The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes. United States. https://doi.org/10.1063/1.3271041
Hayashi, Masahito, Markham, Damian, Murao, Mio, Institute for Nano Quantum Information Electronics, University of Tokyo, Tokyo 113-0033, Owari, Masaki, Virmani, Shashank, and Department Physics, SUPA, University of Strathclyde, Glasgow G4 0NG. 2009. "The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes". United States. https://doi.org/10.1063/1.3271041.
@article{osti_21294514,
title = {The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes},
author = {Hayashi, Masahito and Markham, Damian and Murao, Mio and Institute for Nano Quantum Information Electronics, University of Tokyo, Tokyo 113-0033 and Owari, Masaki and Virmani, Shashank and Department Physics, SUPA, University of Strathclyde, Glasgow G4 0NG},
abstractNote = {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.},
doi = {10.1063/1.3271041},
url = {https://www.osti.gov/biblio/21294514}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 12,
volume = 50,
place = {United States},
year = {Tue Dec 15 00:00:00 EST 2009},
month = {Tue Dec 15 00:00:00 EST 2009}
}