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

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

doi:10.1063/1.3271041

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

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

Physics

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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 language	English
Article number	122104
Number of pages	6
Journal	Journal of Mathematical Physics
Volume	50
Issue number	12
Early online date	28 Dec 2009
DOIs	https://doi.org/10.1063/1.3271041
Publication status	Published - 2009

Keywords

hilbert spaces
measurement theory
quantum entanglement

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10.1063/1.3271041

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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.",

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AU - Murao, Mio

AU - Owari, Masaki

AU - Virmani, Shashank

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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

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VL - 50

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

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

Abstract

Keywords

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