Geodesic
On moduli space of the Wigner quasiprobability distributions for $N$-dimensional quantum systems
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 177-201

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A mapping between operators on the Hilbert space of $N$-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 $SU(N)$ group and a unit $(N-2)$-dimensional sphere. The general consideration is exemplified by a detailed description of the moduli space of $2,3$ and $4$-dimensional systems. 
@article{ZNSL_2018_468_a12,
     author = {V. Abgaryan and A. Khvedelidze and A. Torosyan},
     title = {On moduli space of the {Wigner} quasiprobability distributions for $N$-dimensional quantum systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {177--201},
     publisher = {mathdoc},
     volume = {468},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a12/}
}
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V. Abgaryan; A. Khvedelidze; A. Torosyan. On moduli space of the Wigner quasiprobability distributions for $N$-dimensional quantum systems. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 177-201. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a12/