Non-Markovian quantum trajectories, instruments and time-continuous measurements

TL;DR

This paper investigates whether non-Markovian quantum state diffusion equations can be interpreted as arising from continuous measurements, finding that only the Markovian case generally admits such an interpretation.

Contribution

It provides a necessary criterion for interpreting non-Markovian quantum trajectories as measurement processes, highlighting limitations outside the Markovian regime.

Findings

Normalized linear NMQSD solutions are realizable mainly in the Markovian limit.

The criterion applies to linear NMQSD but not conclusively to nonlinear NMQSD.

Interpretation of nonlinear NMQSD remains an open question.

Abstract

The linear and the nonlinear non-Markovian quantum state diffusion equation (NMQSD) are well known tools for the description of certain non-Markovian open quantum systems. In this work, we systematically investigate whether the normalized linear NMQSD or the nonlinear NMQSD solutions can be generated by means of a time-continuous measurement. By considering any conceivable measurement scheme in the framework of instruments, we derive a necessary criterion for a measurement interpretation of both equations. Concrete examples show that the normalized linear NMQSD solutions are realizable only in the Markovian limit in general. The application of the presented criterion to the nonlinear NMQSD remains an open issue.