Spontaneous wave localization as the solution of the Belavkin-Schrödinger nonlinear filtering equation
In this talk I shall discuss a nonlinear stochastic wave equation derived by the author [1-4] to describe quantum jumps, state diffusion and spontaneous localization of the wave function of a quantum particle under a continuous observation. A dynamical model based on the quantum stochastic endomorphic flow for such open system will be shown and the solution of the reduced quantum filtering equation will be demonstrated on the example of a single quantum particle with a continuous indirect position measurement. I shall also show some open problems and discuss recent applications of the corresponding quantum nonlinear filtering theory in quantum control and communications.
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 V. P. Belavkin: Continuous Non-Demolition Observation, Quantum Filtering and Optimal Estimation. In Quantum Aspects of Optical Communication Lecture notes in Physics 45 131-145, Springer, Berlin 1991. quant-ph/0509205.
 V. P. Belavkin: Quantum Continual Measurements and a Posteriori Collapse on CCR. Communications Mathematical Physics 146 611--635 (1992). math-ph/0512070.