Quantum dynamical entropies for classical stochastic systems

TL;DR

This paper compares two quantum dynamical entropy proposals by extending them to classical stochastic systems, providing explicit formulas and analyzing their information-theoretical implications.

Contribution

It introduces a natural measurement-based approach to stochastic dynamical entropy and compares it with other recent proposals.

Findings

Explicit expression for stochastic dynamical entropy derived

Clear information-theoretical interpretation provided

Comparison with other proposals highlights differences and similarities

Abstract

We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit expression for the stochastic dynamical entropy with a clear information-theoretical interpretation. Finally, we compare our construction with other recent proposals.