Large Deviations at Level 2.5 for Markovian Open Quantum Systems: Quantum Jumps and Quantum State Diffusion

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 Schrodinger equation and we discuss connections of these functionals to optimal control theory.

Automated summary

In this paper, quantum stochastic processes are discussed within a level 2.5 large deviation formalism to characterize fluctuations of time-averaged quantities in the large-time limit. Two classes of quantum stochastic dynamics related to photon detection and homodyne detection are analyzed, presenting the level 2.5 functional derived from the corresponding quantum stochastic Schrodinger equation. Connections to optimal control theory are also discussed for both processes.