Pathwise Solution of a Class of Stochastic Master Equations

Details Pathwise Solution of a Class of Stochastic Master Equations Pathwise Solution of a Class of Stochastic Master Equations

2004-12-15

arxiv.org/abs/quant-ph/0412114v1

J. Opt. B: Quantum Semiclass. Opt. 7 (2005) 293--299

Physics

Quantum Physics

Scientific paper

10.1088/1464-4266/7/9/010

In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is obtained by applying J.M.C. Clark's pathwise reformulation technique from the theory of classical nonlinear filtering. The pathwise versions of the stochastic wave and master equations are defined for all driving paths and depend continuously on them. In the case of white noise equations, we derive analogs of Clark's robust approximations. The results in this paper may be useful for implementing filters for the continuous monitoring and measurement feedback control of quantum systems, and for developing new types of numerical methods for unravelling master equations. The main ideas are illustrated by an example.

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