Quantum relative entropy uncertainty relation
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.
Cite
@article{arxiv.2309.09990,
title = {Quantum relative entropy uncertainty relation},
author = {Domingos S. P. Salazar},
journal= {arXiv preprint arXiv:2309.09990},
year = {2023}
}