  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.
