Communications in Mathematical Physics

, Volume 146, Issue 3, pp 611–635

Quantum continual measurements and a posteriori collapse on CCR


  • V. P. Belavkin
    • Department of MathematicsUniversity of Nottingham

DOI: 10.1007/BF02097018

Cite this article as:
Belavkin, V.P. Commun.Math. Phys. (1992) 146: 611. doi:10.1007/BF02097018


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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© Springer-Verlag 1992