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

TL;DR

This paper evaluates the classicality of qutrit states by computing measures based on the positivity of Wigner functions across three different random ensembles, revealing how classicality indicators vary with parameters.

Contribution

It introduces a comparative analysis of classicality indicators for qutrits across Hilbert-Schmidt, Bures, and Bogoliubov-Kubo-Mori ensembles, highlighting their dependence on state parameters.

Findings

Classicality measures vary significantly across ensembles.

Positivity probability of Wigner functions depends on state stratification.

Different metrics influence the classicality indicators distinctly.

Abstract

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.