294 research outputs found
Nondemolition Principle of Quantum Measurement Theory
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 posteriori
state given by the quantum filtering, i.e., the conditioning of the a priori
induced state on the corresponding reduced algebra. The nonlinear
phenomenological equation of "continuous spontaneous localization" has been
derived from the Schroedinger 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.Comment: 23 pages. See also related papers at
http://www.maths.nott.ac.uk/personal/vpb/research/mes_fou.html and
http://www.maths.nott.ac.uk/personal/vpb/research/cau_idy.htm
Quantum Stochastic Positive Evolutions: Characterization, Construction, Dilation
A characterization of the unbounded stochastic generators of quantum
completely positive flows is given. This suggests the general form of quantum
stochastic adapted evolutions with respect to the Wiener (diffusion), Poisson
(jumps), or general Quantum Noise. The corresponding irreversible Heisenberg
evolution in terms of stochastic completely positive (CP) maps is constructed.
The general form and the dilation of the stochastic completely dissipative (CD)
equation over the algebra L(H) is discovered, as well as the unitary quantum
stochastic dilation of the subfiltering and contractive flows with unbounded
generators. A unitary quantum stochastic cocycle, dilating the subfiltering CP
flows over L(H), is reconstructed.Comment: 33 page
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