Measurements continuous in time and a posteriori states in quantum mechanics

@article{Barchielli1991MeasurementsCI,
  title={Measurements continuous in time and a posteriori states in quantum mechanics},
  author={Alberto Barchielli and Viacheslav P. Belavkin},
  journal={Journal of Physics A: Mathematical and General},
  year={1991},
  volume={24},
  pages={1495-1514}
}
Measurements continuous in time have been consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after a measurement when a certain trajectory of the measured observables is registered (the a posteriori states). In this paper a new derivation of filtering equations is presented for the cases of counting processes and of measurement processes of diffusive type. It… 
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References

SHOWING 1-10 OF 54 REFERENCES

Statistics of continuous trajectories in quantum mechanics: Operation-valued stochastic processes

A formalism developed in previous papers for the description of continual observations of some quantities in the framework of quantum mechanics is reobtained and generalized, starting from a more…

Continuous observations in quantum mechanics: An application to gravitational-wave detectors.

  • Barchielli
  • Physics
    Physical review. D, Particles and fields
  • 1985
A two-stage measuring apparatus for detecting gravitational waves is analyzed using a recently developed formalism for continuous observations in quantum mechanics, obtaining a unified treatment of various models which have appeared in the literature.

Quantum stochastic calculus, operation valued stochastic processes, and continual measurements in quantum mechanics

The physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process (OVSP). In this article, it is shown how…

Measurement theory and stochastic differential equations in quantum mechanics.

  • Barchielli
  • Physics
    Physical review. A, General physics
  • 1986
Continuous (in time) measurements can be introduced in quantum mechanics by using operation-valued measures and quantum stochastic calculus. In this paper quantum stochastic calculus is used for…

Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles.

Stochastic differential equations describing the Markovian evolution of state vectors in the quantum Hilbert space are studied as possible expressions of a universal dynamical principle and the stochastic evolution is proved to induce continuous dynamical reduction of the state vector onto mutually orthogonal subspaces.

Conditional Probability and A Posteriori States in Quantum Mechanics

In order to develop a statistical theory of quantum measurements including continuous observables, a concept of a posteriori states is introduced, which generalizes the notion of regular conditional…

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…

Old and New Ideas in the Theory of Quantum Measurement

The conceptually simplest interpretation of the quantum-mechanical wave function is that adopted by most textbooks. In the celebrated book by Dirac1 one reads — each state of a dynamical system at a…

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…

Quantum stochastic differential equations: an application to the electron shelving effect

By means of a physically interesting example, it is shown how the mathematical theory of quantum stochastic calculus can be used in modelling physical systems. The example is the so-called electron…
...