Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics

TL;DR

This paper extends the quantum jump approach to non-Markovian dynamics by analyzing measurements on bipartite Markovian systems, revealing non-local master equations and non-Markovian effects like information flow.

Contribution

It introduces a consistent framework for non-Markovian quantum jumps based on bipartite Markovian measurements, including renewal and non-renewal processes.

Findings

Non-Markovian effects such as environment-to-system information flow are demonstrated.

A general structure of non-local master equations with non-Markovian unravelings is derived.

The approach applies to two-level systems showing non-Markovian dynamics.

Abstract

The quantum jump approach allows to characterize the stochastic dynamics associated to an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to non-Markovian system dynamics. The results rely in studying a measurement process performed on a bipartite arrangement characterized by a Markovian Lindblad evolution. Both a renewal and non-renewal extensions are found. The general structure of non-local master equations that admit an unravelling in terms of the corresponding non-Markovian trajectories are also found. Studying a two-level system dynamics, it is demonstrated that non-Markovian effects such as an environment-to-system flow of information may be present in the ensemble dynamics.