Entropy fluctuations as a mixedness quantifier

TL;DR

This paper introduces an entropy fluctuation-based measure to quantify the mixedness of quantum states, applicable to both finite and infinite dimensional Hilbert spaces, and useful for identifying effective Hilbert space reductions.

Contribution

It presents a novel mixedness quantifier based on entropy fluctuations, capable of assessing mixedness and Hilbert space reduction in diverse quantum systems.

Findings

The measure indicates maximum mixedness when the state is fully mixed.

It detects effective Hilbert space reduction in atom-field interactions.

Applicable to finite and infinite dimensional Hilbert spaces.

Abstract

We propose a mixedness quantifier based on entropy fluctuations. It provides information about the degree of mixedness either for finite dimensional and infinite dimensional Hilbert spaces. It may be used to determine the reduction of the Hilbert space as it becomes maximum when, either the state is maximally mixed, or, when the Hilbert space effectively reduces its dimensions, such as in the atom field interaction where the two-level atom dictates the final dimension of the field.