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Existence, uniqueness and approximation of the jump-type stochastic Schrödinger equation for two-level systems. (English) Zbl 1204.81110

This is the second part of the author’s work on Belavkin equations. These equations are also called stochastic Schrödinger equations and describe the time evolution of an open quantum system undergoing a continuous quantum measurement. In general, they are not of the usual type and pose tedious problems in terms of mathematical and physical justification.
The diffusive case was considered by the author in a previous paper [Ann. Probab. 36, No. 6, 2332–2353 (2008; Zbl 1167.60006)]. In this article, he concentrates on the Poisson case, which uses some tools from random measure theory. Existence and uniqueness of a weak solution are proved for the associated stochastic jump equation. The convergence of the discrete quantum trajectories to the solution of the Belavkin equation is obtained through a random coupling method and the approximation of the solution by its Euler scheme.

MSC:

81S25 Quantum stochastic calculus
60J75 Jump processes (MSC2010)
60G57 Random measures

Citations:

Zbl 1167.60006
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References:

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