Divergent quantum excess entropy

Investigate the behavior and interpretation of the quantum excess entropy when its defining series diverges, including the implications of infinite excess entropy for quantum stochastic processes.

Background

The paper defines quantum excess entropy as the accumulated finite-window overestimation of the quantum entropy rate. The main results interpret finite quantum excess entropy as a measure of temporal correlations and establish its equivalence to the quantum mutual information across asymptotically long past and future halves.

The authors explicitly restrict their analysis to finite excess entropy. Processes with divergent excess entropy are associated later in the paper with unbounded, long-range temporal correlations and potentially infinite-dimensional or continuously expanding memory, but their mathematical analysis is left unresolved.