Generalized Weyl-Heisenberg algebra, qudit systems and entanglement measure of symmetric states via spin coherent states

Abstract : 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-Heisenberg algebra of finite dimension d. This provides a natural way to deal with the separable and entangled states of a system of N = d-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-Heisenberg 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-Study 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 (i.e., 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.
Complete list of metadatas

Cited literature [58 references]  Display  Hide  Download

http://hal.in2p3.fr/in2p3-01767266
Contributor : Maurice Robert Kibler <>
Submitted on : Monday, April 16, 2018 - 9:24:24 AM
Last modification on : Thursday, February 7, 2019 - 4:57:02 PM

Files

Daoud-Kibler_version 13 04 18....
Files produced by the author(s)

Identifiers

Collections

Citation

Mohammed Daoud, Maurice Robert Kibler. Generalized Weyl-Heisenberg algebra, qudit systems and entanglement measure of symmetric states via spin coherent states. Entropy, MDPI, 2018, 20 (4), pp.292. ⟨10.3390/e20040292⟩. ⟨in2p3-01767266⟩

Share

Metrics

Record views

151

Files downloads

148