Poisson and Diffusion Approximation of Stochastic Schrodinger equations with Control

Abstract

"Quantum trajectories" are solutions of stochastic differential equations of non-usual type. Such equations are called "Belavkin" or "Stochastic Schrödinger Equations" and describe random phenomena in continuous measurement theory of Open Quantum System. Many recent investigations deal with the control theory in such model. In this article, stochastic models are mathematically and physically justified as limit of concrete discrete procedures called "Quantum Repeated Measurements". In particular, this gives a rigorous justification of the Poisson and diffusion approximation in quantum measurement theory with control. Furthermore we investigate some examples using control in quantum mechanics.

38 pages

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Cited by in corpus (6)

• Exponential Stability of Subspaces for Quantum Stochastic Master Equations
• Surpassing the Thermal Cramer-Rao Bound with Collisional Thermometry
• Quantum state engineering by steering in the presence of errors
• Dynamic Quantum Games
• Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements
• The law of large numbers for quantum stochastic filtering and control of many particle systems