Thermodynamic uncertainty relation for quantum first-passage processes

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 jump events, 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.

Automated summary

We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains, and obtain bounds for the observables using the Loschmidt echo. We show that the lower bound corresponds to the quantum Fisher information and reduce the bound to a thermodynamic uncertainty relation for classical first passage processes in classical dynamics.