Quantum relative entropy uncertainty relation

• URL: http://arxiv.org/abs/2309.09990v2
• Date: Tue, 26 Sep 2023 16:57:59 GMT
• Title: Quantum relative entropy uncertainty relation
• Authors: Domingos S. P. Salazar
• Abstract summary: For classic systems, the fluctuations of a current have a lower bound in terms of the entropy production. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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