Stopping times for quantum Markov chains

Ameur Dhahri, Franco Fagnola

Carlos F. Lardizabal

Abdessatar Souissi

In the present paper, we introduce stopping rules and related notions for quantum Markov chains on trees (QMCT). We prove criteria for recurrence, accessibility and irreducibility for QMCT. This work extends to trees the notion of stopping times for quantum Markov chains (QMC) introduced by Accardi and Koroliuk, which plays a key role in the study of many properties of QMC. Moreover, we illustrate the obtained results for a concrete model of XY-Ising type.

Burkhard Kümmerer

Luigi Accardi, Dmitri Koroliouk

Yoshihiko Hasegawa

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.