A Stochastic Schr\"odinger Equation for the Generalized Rate Operator Unravelings

TL;DR

This paper derives a stochastic Schrödinger equation for the generalized rate operator unraveling formalism, enhancing simulation efficiency and providing a method to detect unphysical quantum evolutions.

Contribution

It introduces a stochastic Schrödinger equation for the generalized rate operator unraveling, applicable with and without reverse jumps, and proposes a way to identify unphysical master equations.

Findings

Derived a stochastic Schrödinger equation for the formalism.

Showed the method's ability to detect unphysical time evolutions.

Improved simulation efficiency for certain quantum dynamics.

Abstract

Stochastic unravelings are a widely used tool to solve open quantum system dynamics, in which the exact solution is obtained via an average over a stochastic process on the set of pure quantum states. Recently, the generalized rate operator unraveling formalism was derived, allowing not only for an engineering of the stochastic realizations, but also to unravel without reverse jumps even for some dynamics in which P-divisibility is violated, thus hugely improving the simulation efficiency. This is possible because the unraveling depend on an arbitrary non-linear transformation which can incorporate the memory effects. In this work, a stochastic Schr\"odinger equation for this formalism is derived, both for cases with and without reverse jumps. It is also shown that a failure of this method can be used to witness master equations leading unphysical time evolutions, independently on the particular non-linear transformation considered.