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Foundations of Physics

, Volume 24, Issue 5, pp 685–714 | Cite as

Nondemolition principle of quantum measurement theory

  • V. P. Belavkin
Article

Abstract

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The “collapsed state-vector” after the “objectification” is simply treated as a random vector of the a posterioristate given by the quantum filtering, i.e., the conditioning of the a prioriinduced state on the corresponding reduced algebra. The nonlinear phenomenological equation of “continuous spontaneous localization” has been derived from the Schrödinger equation as a case of the quantum filtering equation for the diffusive nondemolition measurement. The quantum theory of measurement and filtering suggests also another type of the stochastic equation for the dynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum experiments.

Keywords

Quantum Theory Random Vector Dynamical Theory Measurement Theory Quantum Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. P. Belavkin
    • 1
    • 2
  1. 1.Fachbereich PhysikPhilipps UniversitätMarburgGermany
  2. 2.Mathematics DepartmentUniversity of NottinghamUK

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