# An upper bound for the KS-entropy in quantum mixing systems

## TL;DR

This paper derives an upper bound for the Kolmogorov-Sinai entropy in quantum mixing systems using quantum phase space graininess, a rescaled entropy, and correlation properties, linking classical and quantum chaos features.

## Contribution

It introduces a novel method to estimate the KS-entropy upper bound in quantum systems considering quantum phase space graininess and mixing correlations.

## Key findings

- Derived an upper bound for quantum KS-entropy.
- Linked quantum mixing properties with classical ergodic hierarchy.
- Identified the quantum logarithmic timescale in chaotic systems.

## Abstract

We present an upper bound for the Kolmogorov-Sinai entropy of quantum systems having a mixing quantum phase space. The method for this estimation is based on the following ingredients: i) the graininess of quantum phase space in virtue of the Uncertainty Principle, ii) a time rescaled KS-entropy that introduces the characteristic timescale as a parameter, and iii) the factorization property of the mixing correlations. The analogy between the structures of the mixing level of the ergodic hierarchy and of its quantum counterpart is shown. Moreover, the logarithmic timescale, characteristic of quantum chaotic systems, is obtained.