Stochastic unravelings for Heisenberg picture and trace-nonpreserving dynamics

TL;DR

This paper introduces a versatile stochastic unraveling framework for simulating arbitrary trace-nonpreserving open quantum system dynamics, broadening the scope of stochastic methods beyond traditional trace-preserving cases.

Contribution

It extends piecewise-deterministic unravelings to handle general trace-nonpreserving master equations, including Heisenberg picture evolutions and non-Hermitian dynamics.

Findings

Framework includes unravelings of arbitrary dynamics in the Heisenberg picture.

Applicable to trace-decreasing and trace-increasing processes via stochastic disappearance and replication.

Compatible with different unraveling schemes and non-Markovian reverse jumps.

Abstract

Stochastic unravelings allow to efficiently simulate open system dynamics, yet their application has traditionally been restricted to master equations that preserve both Hermiticity and trace. In this work, we introduce a general framework that extends piecewise-deterministic unravelings to arbitrary trace-nonpreserving master equations, requiring only positivity and Hermiticity of the dynamics. Our approach includes, as special cases, unravelings of arbitrary dynamics in the Heisenberg picture, evolutions interpolating between fully Lindblad and non-Hermitian Hamiltonian generators, and equations employed in the derivation of full counting statistics, for which we show it can be used to obtain the moments of the associated probability distribution. The framework is suitable for both trace-decreasing and trace-increasing processes through stochastic disappearance and replication of the stochastic realizations, and it is compatible with different unraveling schemes and with reverse jumps in the non-Markovian regime. Thereby, our approach provides a powerful and versatile simulation method that significantly broadens the applicability of stochastic techniques for open system dynamics.