Patterns in the jump-channel statistics of open quantum systems

TL;DR

This paper characterizes the statistical patterns of emitted symbols in open quantum systems with multiple jump channels, revealing structures like closed patterns and state clustering, with applications to quantum spin chains.

Contribution

It provides a comprehensive characterization of the stochastic process of emitted symbols, including simulation methods and pattern detection techniques in open quantum systems.

Findings

Identification of closed and recurring patterns in jump-channel statistics

Development of methods to cluster states based on predictability

Application to transport in a boundary-driven XY spin chain

Abstract

A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time distributions, very little is known about the statistics of the emitted symbols. In this letter we fill in this gap. First, we provide a full characterization of the resulting stochastic process, including efficient ways of simulating it, as well as determining the underlying memory structure. Second, we show how to unveil patterns in the stochastic evolution: Some systems support closed patterns, wherein the evolution runs over a finite set of states, or at least recurring states. But even if neither is possible, we show that one may still cluster the states approximately, based on their ability to predict future outcomes. We illustrate these ideas by studying transport through a boundary-driven one-dimensional XY spin chain.