{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T22:15:34Z","timestamp":1774995334420,"version":"3.50.1"},"reference-count":61,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,17]],"date-time":"2018-04-17T00:00:00Z","timestamp":1523923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A relation is established in the present paper between Dicke states in a d-dimensional space and vectors in the representation space of a generalized Weyl\u2013Heisenberg algebra of finite dimension d. This provides a natural way to deal with the separable and entangled states of a system of    N = d \u2212 1    symmetric qubit states. Using the decomposition property of Dicke states, it is shown that the separable states coincide with the Perelomov coherent states associated with the generalized Weyl\u2013Heisenberg algebra considered in this paper. In the so-called Majorana scheme, the qudit (d-level) states are represented by N points on the Bloch sphere; roughly speaking, it can be said that a qudit (in a d-dimensional space) is describable by a N-qubit vector (in a N-dimensional space). In such a scheme, the permanent of the matrix describing the overlap between the N qubits makes it possible to measure the entanglement between the N qubits forming the qudit. This is confirmed by a Fubini\u2013Study metric analysis. A new parameter, proportional to the permanent and called perma-concurrence, is introduced for characterizing the entanglement of a symmetric qudit arising from N qubits. For    d = 3    (    \u21d4 N = 2    ), this parameter constitutes an alternative to the concurrence for two qubits. Other examples are given for    d = 4    and 5. A connection between Majorana stars and zeros of a Bargmmann function for qudits closes this article.<\/jats:p>","DOI":"10.3390\/e20040292","type":"journal-article","created":{"date-parts":[[2018,4,18]],"date-time":"2018-04-18T03:51:13Z","timestamp":1524023473000},"page":"292","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Generalized Weyl\u2013Heisenberg Algebra, Qudit Systems and Entanglement Measure of Symmetric States via Spin Coherent States"],"prefix":"10.3390","volume":"20","author":[{"given":"Mohammed","family":"Daoud","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Sciences Ain Chock, University Hassan II, Casablanca 91 000, Morocco"},{"name":"Groupe Th\u00e9orie, Institut de Physique Nucl\u00e9aire, CNRS\/IN2P3, 69622 Villeurbanne, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8522-4561","authenticated-orcid":false,"given":"Maurice R.","family":"Kibler","sequence":"additional","affiliation":[{"name":"Groupe Th\u00e9orie, Institut de Physique Nucl\u00e9aire, CNRS\/IN2P3, 69622 Villeurbanne, France"},{"name":"Facult\u00e9 des Sciences et Technologies, Universit\u00e9 Claude Bernard Lyon 1, 69622 Villeurbanne, France"},{"name":"IDEXLYON, Universit\u00e9 de Lyon, 69361 Lyon, France"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/S0375-9601(03)00941-1","article-title":"The Bloch vector for N-level systems","volume":"314","author":"Kimura","year":"2003","journal-title":"Phys. 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