Non-Markovian Open Quantum Systems: Input-Output Fields, Memory, Monitoring

TL;DR

This paper analyzes monitoring techniques for non-Markovian open quantum systems, demonstrating how the environment's field representation allows for separating memory effects and enabling standard Markovian monitoring methods.

Contribution

It introduces a framework that treats the system-plus-memory as Markovian and develops a non-Markovian stochastic Schrödinger equation for such systems.

Findings

System-plus-memory becomes Markovian in the field representation.

Only the mixed state of the system can be predicted, not the pure state.

A non-Markovian stochastic Schrödinger equation is derived.

Abstract

Principles of monitoring non-Markovian open quantum systems are analyzed. We use the field representation of the environment (Gardiner and Collet, 1985) for the separation of its memory and detector part, respectively. We claim the system-plus-memory compound becomes Markovian, the detector part is tractable by standard Markovian monitoring. Because of non-Markovianity, only the mixed state of the system can be predicted, the pure state of the system can be retrodicted. We present the corresponding non-Markovian stochastic Schr\"odinger equation.