On moduli space of the Wigner quasiprobability distributions for $N$-dimensional quantum systems
Quantum Physics
2018-09-17 v1 Mathematical Physics
math.MP
Abstract
A mapping between operators on the Hilbert space of -dimensional quantum system and the Wigner quasiprobability distributions defined on the symplectic flag manifold is discussed. The Wigner quasiprobability distribution is constructed as a dual pairing between the density matrix and the Stratonovich-Weyl kernel. It is shown that the moduli space of the Stratonovich-Weyl kernel is given by an intersection of the coadjoint orbit space of the group and a unit -dimensional sphere. The general consideration is exemplified by a detailed description of the moduli space of 2, 3 and 4-dimensional systems.
Keywords
Cite
@article{arxiv.1809.05166,
title = {On moduli space of the Wigner quasiprobability distributions for $N$-dimensional quantum systems},
author = {Vahagn Abgaryan and Arsen Khvedelidze and Astghik Torosyan},
journal= {arXiv preprint arXiv:1809.05166},
year = {2018}
}