Thermodynamic uncertainty relation for quantum first passage process via Loschmidt echo
Yoshihiko Hasegawa · arXiv (Cornell University) · 2021
We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains. We consider first passage processes stopping after a fixed number of jumps, which contrasts with typical quantum Markov chains which end at a fixed time. We bound observables of 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 of the bound, we show that the lower bound corresponds to the quantum Fisher information, which has played a fundamental role in uncertainty relations in quantum systems. Moreover, our bound reduces to a thermodynamic uncertainty relation for classical first passage processes when considering classical dynamics.