Quantum thermodynamic uncertainty relations without quantum corrections: A coherent-incoherent correspondence approach

TL;DR

This paper introduces a novel framework called coherent-incoherent correspondence to derive quantum thermodynamic uncertainty relations without quantum corrections, enabling better inference of entropy production in quantum systems.

Contribution

The paper presents a new approach that maps quantum systems to classical-like incoherent systems to derive uncertainty relations without quantum correction terms.

Findings

Steady-state coherence reduces bounds on precision.

The method allows inference of entropy production from current statistics.

The approach is validated through numerical models with coherent jump operators.

Abstract

We introduce the coherent-incoherent correspondence as a framework for deriving quantum thermodynamic uncertainty relations under continuous measurement in Lindblad dynamics. The coherent-incoherent correspondence establishes a mapping between the original quantum system that undergoes \textit{ coherent} evolution and its corresponding \textit{incoherent} system without coherent dynamics. The coherent-incoherent correspondence relates quantities across these two systems, including jump statistics, dynamical activity, and entropy production. Since the classical-like properties of the incoherent system allow us to derive thermodynamic uncertainty relations within it, these relations can be transferred to the coherent system via the coherent-incoherent correspondence. This enables us to derive quantum thermodynamic uncertainty relations for the original coherent system. Unlike existing quantum uncertainty relations, which typically require explicit quantum correction terms, our approach avoids these additional terms. This means that we can establish a lower bound for quantum entropy production using only current statistics. This approach opens up new possibilities for inferring entropy production in quantum systems. Through numerical calculations for a model with coherent jump operators, we show that steady-state coherence lowers the bounds on precision (i.e., allows higher precision).