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. *
The separable mixed 2-qubit X−states are classified in accordance with degeneracies in the spectrum of density matrices. It is shown that there are four classes of separable X−states, among them: one 4D family, a pair of 2D family and a single, zero-dimensional maximally mixed state. arXiv:1609.06209v1 [quant-ph]
In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the dependence of the global indicator of classicality on the assigned geometry of a quantum state space is analysed for a whole family of Wigner quasiprobability representations. General considerations are exemplified by constructing the global indicator of classicality/quantumness for the Hilbert-Schmidt, Bures and Bogoliubov-Kubo-Mori ensembles of qubits and qutrits.
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