NONDEMOLITION PRINCIPLE OF QUANTUM MEASUREMENT THEORY

We give an explicit axiomatic formulation of the quantum measurement t heory which is free of the projection postulate. It is based on the ge neralized nondemolition principle applicable also to the unsharp, cont inuous-spectrum and continuous-in-time observations. The ''collapsed s tate-vector'' after the ''objectification'' is simply treated as a ran dom vector of the a posteriori state given by the quantum filtering, i .e., the conditioning of the a priori induced state on the correspondi ng reduced algebra. The nonlinear phenomenological equation of ''conti nuous spontaneous localization'' has been derived from the Schrodinger equation as a case of the quantum filtering equation for the diffusiv e nondemolition measurement. The quantum theory of measurement and fil tering suggests also another type of the stochastic equation for the d ynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum exp eriments.