Nondemolition principle of quantum measurement theory

@article{Belavkin1994NondemolitionPO,
  title={Nondemolition principle of quantum measurement theory},
  author={Viacheslav P. Belavkin},
  journal={Foundations of Physics},
  year={1994},
  volume={24},
  pages={685-714}
}
  • V. Belavkin
  • Published 1 May 1994
  • Physics
  • Foundations of Physics
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… 
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References

SHOWING 1-10 OF 59 REFERENCES
Quantum Theory of Measurement
Quantum mechanics was discovered sixty-one years ago in 1925. It began with Heisenberg’s introduction of matrix mechanics, which was followed by Schrodinger finding his wave equation. Then Dirac gave…
Nondemolition observation of a free quantum particle.
TLDR
It is shown that the dispersion of the wave packet does not increase to in½nity like for the free unobserved particle but tends to the …nite limit 1 = (~=2 m) where is the accuracy coe¢ cient of an indirect nondemolition measurement of the particle position, and ~ is Planck constant.
Quantum measuring processes of continuous observables
The purpose of this paper is to provide a basis of theory of measurements of continuous observables. We generalize von Neumann’s description of measuring processes of discrete quantum observables in…
Non-Demolition Measurement and Control in Quantum Dynamical Systems
A multi-stage version of the theory of quantum-mechanical measurements and quantum-statistical decisions applied to the non-demolition control problem for quantum objects is developed. It is shown…
Models for universal reduction of macroscopic quantum fluctuations.
  • Diósi
  • Physics
    Physical review. A, General physics
  • 1989
TLDR
A new parameter-free unification of micro- and macrodynamics is constructed and gravitational measures for reducing macroscopic quantum fluctuations of the mass density are applied to lead to classical trajectories in the Macroscopic limit of translational motion.
Quantum stochastic calculus and quantum nonlinear filtering
Reconstruction theorem for a quantum stochastic process
This paper gives a physically interpretable--in real time--definition of a QSP as families of representations of the observable algebra 'B' in a common (large) system by indicating a universal method…
Approximate measurement in quantum mechanics. II
An approximate measurement procedure of the following type is considered: (i) An initial eigenstate of the object observable leads to a final statistical operator of the object plus apparatus…
An operational approach to quantum probability
In order to provide a mathmatical framework for the process of making repeated measurements on continuous observables in a statistical system we make a mathematical definition of an instrument, a…
Generalisation of Wigner's theorem for dissipative quantum systems
The author presents a quantum Langevin equation in the Schrodinger picture. The friction term is motivated by a natural generalisation of Wigner's theorem or, equivalently, of Dirac's superposition…
...
...