Semi-Markov Processes in Open Quantum Systems. II. Counting Statistics with Resetting

TL;DR

This paper extends semi-Markov process methods to include resetting in open quantum systems, enabling calculation of counting statistics despite the complexity introduced by resets and wave function collapses.

Contribution

It introduces a novel approach to derive counting statistics in reset quantum systems using survival and waiting-time distributions, along with a continuous-time cloning algorithm for large-deviation analysis.

Findings

Derived exact tilted matrix equation for reset quantum systems

Demonstrated methods on quantum optics systems

Enabled counting statistics without explicit quantum operator inputs

Abstract

A semi-Markov process method for obtaining general counting statistics for open quantum systems is extended to the scenario of resetting. The simultaneous presence of random resets and wave function collapses means that the quantum jump trajectories are no longer semi-Markov. However, focusing on trajectories and using simple probability formulas, general counting statistics can still be constructed from reset-free statistics. An exact tilted matrix equation is also obtained. The inputs of these methods are the survival distributions and waiting-time density distributions instead of quantum operators. In addition, a continuous-time cloning algorithm is introduced to simulate the large-deviation properties of open quantum systems. Several quantum optics systems are used to demonstrate these results.