Large deviations at level 2.5 for Markovian open quantum systems: quantum jumps and quantum state diffusion

TL;DR

This paper develops a comprehensive large deviation framework at level 2.5 for Markovian open quantum systems, analyzing quantum jumps and quantum state diffusion, and linking fluctuations to optimal control theory.

Contribution

It introduces an explicit level 2.5 large deviation formalism for quantum stochastic processes, covering quantum jump trajectories and quantum state diffusion.

Findings

Derived the level 2.5 functional from quantum stochastic Schrödinger equations.

Connected large deviation functionals to optimal control theory.

Provided a complete characterization of fluctuations in quantum trajectories.

Abstract

We consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. The first class consists of the quantum jump trajectories related to photon detection; the second is quantum state diffusion related to homodyne detection. For both processes, we present the level 2.5 functional starting from the corresponding quantum stochastic Schr\"odinger equation and we discuss connections of these functionals to optimal control theory.