Thermodynamic uncertainty relation for quantum first passage process

TL;DR

This paper establishes a thermodynamic uncertainty relation for quantum first passage processes in quantum Markov chains, linking irreversibility, quantum Fisher information, and classical limits.

Contribution

It introduces a novel uncertainty relation for quantum first passage processes, connecting irreversibility measures with quantum Fisher information and classical bounds.

Findings

Bounds for observables using Loschmidt echo

Lower bound corresponds to quantum Fisher information

Reduces to classical thermodynamic uncertainty relation

Abstract

We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains. We consider first passage processes that stop after a fixed number of jumps, which contrasts with typical quantum Markov chains which end at a fixed time. We obtain bounds for the observables of the first passage processes in quantum Markov chains by the Loschmidt echo, which quantifies the extent of irreversibility in quantum many-body systems. Considering a particular case, we show that the lower bound corresponds to the quantum Fisher information, which plays a fundamental role in uncertainty relations in quantum systems. Moreover, considering classical dynamics, our bound reduces to a thermodynamic uncertainty relation for classical first passage processes.