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 that in Gaussian case of quantum one-dimensional linear Markovian dynamical system with a quantum linear transmission line optimal quantum multistage decision rule consists of classical linear optimal control strategy and quantum optimal filtering procedure, the latter contains the optimal quantum coherent measurement on the output of the line and the recursive processing by Kalman-Busy filter. All the results are illustrated by an example of the optimal problem solution for a quantum one-dimensional linear oscillator on the input of a quantum wave transmission line.
KeywordsQuantum Oscillator Optimal Quantum Optimal Observation Coherent Measurement Quantum Stochastic Differential Equation
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- 1.Belavkin, V.P.: To the theory of control in quantum observable systems, Automic and Remove Control, 2(1983).Google Scholar
- 4.Belavkin, V.P.: An operational theory of quantum stochastic processes, Proc. of VII-th Conference on Coding and Inform.Trans.Theory, Moscow-Vilnus, 1978.Google Scholar
- 9.Butkovski, A.G. and U.J. Samoilenko: Control of quantum mechanical processes, Nauka, Moscow 1984.Google Scholar
- 12.Accardi, L. and K.R. Parthasaraty: Quantum stochastic calculung. Springer LNM (to appear).Google Scholar
- 13.Belavkin, V.P.: Optimal measurement and control in quantum dynamical systems, Preprint N411, UMK, Torun, 1979.Google Scholar
- 14.Belavkin, V.P.: Optimization of quantum observation and control, Lecture Notes in Control and Inform. Sciences, IFIP, Optimization Techniques, Warsaw, 1979, Parti, Springer-Verlag.Google Scholar
- 15.Holevo, A.S.: Investigations on general statistical decision theory, Proc. of MIAN, CXXIV, Nauka, Moscow, 1976.Google Scholar
- 17.Klauder, J.R. and E.C.D. Sudarshan:: Fundamentals of quantum optics. W.A.Benjamin, inc. New York, Amsterdam 1968.Google Scholar
- 19.Lax, M.: Quantum noise IV. Quantum theory of noise sources. Phys.Pev., vol. 145, pp. 1599–1611, 1965.Google Scholar