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Optimization of quantum observation and control

  • V. P. Belavkin
Stochastic Control
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 22)

Abstract

A multi-stage version of the statistical decision theory applied to the optimal control problem in a Markovian dynamical system with quantum-mechanical observation is developed. Quantum analogies of Stratonovich non-stationary discrete filtering and Bellman quantum dynamical programming are obtained. It is shown that optimal strategy in Gaussian case of linearly controlled system observed by means of a quantum linear communication channel and mean square criteria consists of a sequence of quantum coherent measurements, the data of which are processed by Kalman filter, and classical linear optimal decision rule.

Keywords

Kalman Filter Decision Theory Gaussian Case Statistical Decision Theory Optimal Decision Rule 
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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References

  1. 1.
    Helstrom C.W., Quantum Detection and Estimation Theory, Academic Press, N.York 1976.Google Scholar
  2. 2.
    Belavkin V.P., Optimal Quantum Filtering of Markov Signals, Problems of Control and Information Theory, vol.5, 1978.Google Scholar
  3. 3.
    Belavkin V.P., An Operational Theory of Quantum Stochastic Processes, Proc. of VII-th Conference on Coding and Information Transmission Theory, Moscow-Vilnus 1978 (in Russian).Google Scholar
  4. 4.
    Belavkin V.P., Optimal Measurement and Control in Quantum Dynamical Systems, Preprint UMK 412, Torun 1979.Google Scholar
  5. 5.
    Stratonovich R.L., Conditional Markov processes and their applications to optimal control, Moscow State University, Moscow 1966.Google Scholar
  6. 6.
    Holevo A.S., Investigations on general statistical decision theory, Proc. of MIAN, CXXIV, Nauka, Moscow 1976.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • V. P. Belavkin
    • 1
  1. 1.Moscow Electronic Machine InstituteMoscowUSSR

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