Comparing classicality of qutrits from Hilbert–Schmidt, Bures and Bogoliubov–Kubo–Mori ensembles

In the report we analyze the indicator/measure of classicality of quantum states defined as the probability to find a state with a positive Wigner function within a unitary invariant random ensemble. The indicators of classicality of three ensembles associated with the Hilbert–Schmidt, Bures and Bogoliubov–Kubo–Mori metrics on the space of quantum states of 3-level system are computed. Their dependence on a moduli parameter of the Wigner function is studied for all strata of a qutrit state space stratified in accordance with the unitary group action.