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

Masahito Hayashi, Damian Markham, Mio Murao, Masaki Owari, Shashank Virmani

Research output: Contribution to journalArticle

31 Citations (Scopus)
7 Downloads (Pure)

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.
Original languageEnglish
Article number122104
Number of pages6
JournalJournal of Mathematical Physics
Volume50
Issue number12
Early online date28 Dec 2009
DOIs
Publication statusPublished - 2009

Fingerprint

Pure State
Entanglement
Non-negative
products
Symmetric Product
Fidelity

Keywords

  • hilbert spaces
  • measurement theory
  • quantum entanglement

Cite this

Hayashi, Masahito ; Markham, Damian ; Murao, Mio ; Owari, Masaki ; Virmani, Shashank. / The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes. In: Journal of Mathematical Physics. 2009 ; Vol. 50, No. 12.
@article{c02e6fd26aff4e458a5b17f8e218d1a6,
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.",
keywords = "hilbert spaces, measurement theory, quantum entanglement",
author = "Masahito Hayashi and Damian Markham and Mio Murao and Masaki Owari and Shashank Virmani",
year = "2009",
doi = "10.1063/1.3271041",
language = "English",
volume = "50",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
number = "12",

}

The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes. / Hayashi, Masahito; Markham, Damian; Murao, Mio; Owari, Masaki; Virmani, Shashank.

In: Journal of Mathematical Physics, Vol. 50, No. 12, 122104, 2009.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes

AU - Hayashi, Masahito

AU - Markham, Damian

AU - Murao, Mio

AU - Owari, Masaki

AU - Virmani, Shashank

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - hilbert spaces

KW - measurement theory

KW - quantum entanglement

U2 - 10.1063/1.3271041

DO - 10.1063/1.3271041

M3 - Article

VL - 50

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

M1 - 122104

ER -