New results unearthed from urtexts of quantum state diffusion

TL;DR

This paper extends the theory of quantum state diffusion to all positive dynamics, not just the complete-positive subclass, highlighting the importance of the transition rate operator and invariant approaches.

Contribution

It introduces a comprehensive description of all diffusive unravelings of positive quantum dynamics, broadening the scope beyond traditional complete-positive cases.

Findings

Extended quantum state diffusion beyond complete-positive dynamics

Identified the role of the transition rate operator in unravelings

Provided invariant, representation-independent formulations

Abstract

Thirty years ago, the present author discussed pure state unraveling (stochastic quantum trajectories) of Markovian open system dynamics. The fact that he considered all positive dynamics, not restricted for the Lindblad-Gorini-Kossakowski-Sudarshan complete-positive subclass, has remained unnoticed so far. Here we point out the importance of the transition rate operator and the merit of invariant (representation-independent) approach, with reference to invariant condition of positive dynamics and extension of quantum state diffusion beyond complete-positive dynamics. A new result, description of all diffusive unravelings of positive dynamics directly follows.