Stochastic unraveling of positive quantum dynamics

TL;DR

This paper generalizes quantum state diffusion to include positive but not completely positive dynamics, enabling more accurate modeling of certain open quantum systems.

Contribution

It introduces a new stochastic unraveling method applicable to positive, non-completely positive evolutions, extending standard QSD techniques.

Findings

Successfully applied to exciton transfer models

Captures phenomena missed by standard completely positive approaches

Provides a framework for non-completely positive quantum dynamics

Abstract

Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a generalization of QSD, which also applies to positive, but not completely positive evolutions. The rate and the action of the diffusive processes involved in the unraveling are obtained by applying a proper transformation to the operators which define the master equation. The unraveling is first defined for semigroup dynamics and then extended to a definite class of time-dependent generators. We test our approach on a prototypical model for the description of exciton transfer, keeping track of relevant phenomena, which are instead disregarded within the standard, completely positive framework.