Quantum relative entropy uncertainty relation

TL;DR

This paper generalizes the thermodynamic uncertainty relation to quantum systems, establishing a lower bound on the uncertainty of quantum observables based on quantum relative entropy, applicable to diverse dynamics and environments.

Contribution

It introduces a quantum uncertainty relation derived from quantum relative entropy, extending classical thermodynamic bounds to quantum regimes.

Findings

Derived a quantum uncertainty relation using quantum relative entropy.

Applicable to arbitrary quantum dynamics and non-thermal environments.

Provides a new bound linking quantum observable fluctuations to quantum entropy production.

Abstract

For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and non-thermal environments.