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Generalized Weyl-Heisenberg Algebra, Qudit Systems and Entanglement Measure of Symmetric States via Spin Coherent States. Part II: The Perma-Concurrence Parameter

1
Department of Physics, Faculty of Sciences, University Ibn Tofail, BP 133 Kénitra, Morocco
2
CNRS/IN2P3, Institut de Physique Nucléaire, 69622 Villeurbanne, France
3
Faculté des Sciences et Technologies, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
4
IDEXLYON, Université de Lyon, 69361 Lyon, France
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 875; https://doi.org/10.3390/sym11070875
Received: 14 June 2019 / Accepted: 27 June 2019 / Published: 3 July 2019
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Abstract

This paper deals with separable and entangled qudits | ψ d (quantum states in dimension d) constructed from Dicke states made of N = d 1 qubits. Such qudits present the property to be totally symmetric under the interchange of the N qubits. We discuss the notion of perma-concurrence P d for the qudit | ψ d , introduced by the authors (Entropy 2018, 20, 292), as a parameter for characterizing the entanglement degree of | ψ d . For d = 3 , the perma-concurrence P 3 constitutes an alternative to the concurrence C for symmetric two-qubit states. We give several expressions of P d (in terms of matrix permanent and in terms of unit vectors of R 3 pointing on the Bloch sphere) and precise the range of variation of P d (going from separable to maximally entangled states). Numerous examples are presented for P d . Special attention is devoted to states of W type and to maximally entangled states of Bell and Greenberger–Horne–Zeilinger type. View Full-Text
Keywords: generalized Weyl-Heisenberg algebra; qubits and qudits; Dicke states; SU(2) coherent states; entanglement; concurrence; perma-concurrence; Majorana stars generalized Weyl-Heisenberg algebra; qubits and qudits; Dicke states; SU(2) coherent states; entanglement; concurrence; perma-concurrence; Majorana stars
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Daoud, M.; Kibler, M.R. Generalized Weyl-Heisenberg Algebra, Qudit Systems and Entanglement Measure of Symmetric States via Spin Coherent States. Part II: The Perma-Concurrence Parameter. Symmetry 2019, 11, 875.

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