Appropriate ensemble selection for different physical systems

Determine which metric-induced random density matrix ensembles, drawn from the family of monotone information-geometric metrics over density matrices (including but not limited to the Hilbert–Schmidt, Bures–Hall, and Bogoliubov–Kubo–Mori metrics), are most appropriate for characterising randomness in different classes of physical quantum systems.

Background

The paper reviews existing geometric-induced ensembles over quantum states, notably the Hilbert–Schmidt and Bures–Hall measures, and introduces a new entropy-based ensemble derived from the Bogoliubov–Kubo–Mori (BKM) metric. While many monotone information metrics can induce distinct random state ensembles, it is not yet clear which of these best capture randomness for various physical settings.

This open question motivates the exploration of additional ensembles beyond the standard Hilbert–Schmidt and Bures–Hall constructions and underpins the authors’ proposal of an entropy-based ensemble as a potentially more suitable prior in certain high-purity regimes.