How to design quantum-jump trajectories via distinct master equation representations

TL;DR

This paper explores the inherent freedom in designing quantum-jump unravelings of open quantum systems, showing how different master equation representations lead to qualitatively distinct stochastic descriptions, with implications for theory and simulation.

Contribution

It introduces a method to construct diverse quantum-jump trajectories by assigning master equation terms differently, utilizing rate operators and dissipativity for classification.

Findings

Multiple unravelings exist for the same open-system dynamics.

A fixed basis of post-jump states can be chosen under certain conditions.

Deterministic evolution can be governed by a non-Hermitian Hamiltonian even with external driving.

Abstract

Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing on quantum-jump unravelings, we demonstrate that there exists inherent freedom in how to assign the terms of the underlying master equation to the deterministic and jump parts of the stochastic description, which leads to a number of qualitatively different unravelings. As relevant examples, we show that a fixed basis of post-jump states can be selected under some definite conditions, or that the deterministic evolution can be set by a chosen time-independent non-Hermitian Hamiltonian, even in the presence of external driving. Our approach relies on the definition of rate operators, whose positivity equips each unraveling with a continuous-measurement scheme and is related to a long known but so far not widely used property to classify quantum dynamics, known as dissipativity. Starting from formal mathematical concepts, our results allow us to get fundamental insights into open quantum system dynamics and to enrich their numerical simulations.