Universal and nonuniversal probability laws in Markovian open quantum dynamics subject to generalized reset processes

TL;DR

This paper explores universal probability laws in Markovian open quantum systems with stochastic resets, revealing conditions under which certain trajectory observables follow observable-independent laws, extending classical results to quantum dynamics.

Contribution

It demonstrates the emergence of universal probability laws in quantum jump trajectories with resets, including conditions for universality in quantum and state-dependent reset processes.

Findings

Universal laws for ordering probabilities in quantum trajectories

Universality independent of observable for certain functions and Poissonian resets

Loss of universality in jump counting observables unless reset rate is very low

Abstract

We consider quantum jump trajectories of Markovian open quantum systems subject to stochastic in time resets of their state to an initial configuration. The reset events provide a partitioning of quantum trajectories into consecutive time intervals, defining sequences of random variables from the values of a trajectory observable within each of the intervals. For observables related to functions of the quantum state, we show that the probability of certain orderings in the sequences obeys a universal law. This law does not depend on the chosen observable and, in case of Poissonian reset processes, not even on the details of the dynamics. When considering (discrete) observables associated with the counting of quantum jumps, the probabilities in general lose their universal character. Universality is only recovered in cases when the probability of observing equal outcomes in a same sequence is vanishingly small, which we can achieve in a weak reset rate limit. Our results extend previous findings on classical stochastic processes [N.~R.~Smith et al., EPL {\bf 142}, 51002 (2023)] to the quantum domain and to state-dependent reset processes, shedding light on relevant aspects for the emergence of universal probability laws.