Abstract
A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior evolution of a quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Langevin evolution equation is solved for the case of a quasi-free Hamiltonian in the initial CCR algebra with a linear output channel, and the posterior dynamics corresponding to an initial Gaussian state is found. It is shown for an example of the posterior dynamics of a quantum oscillator that any mixed state under a complete nondemolition measurement collapses exponentially to a pure Gaussian one.
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Communicated by H. Araki
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Belavkin, V.P. Quantum continual measurements and a posteriori collapse on CCR. Commun.Math. Phys. 146, 611–635 (1992). https://doi.org/10.1007/BF02097018
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DOI: https://doi.org/10.1007/BF02097018