English

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 NN-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 SU(N)SU(N) group and a unit (N2)(N-2)-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}
}