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Statistical decision theory for quantum systems

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  • Holevo, A. S.

Abstract

Quantum statistical decision theory arises in connection with applied problems of optimal detection and processing of quantum signals. In this paper we give a systematic treatment of this theory, based on operator-valued measures. We study the existence problem for optimal measurements and give sufficient and necessary conditions for optimality. The notion of the maximum likelihood measurement is introduced and investigated. The general theory is then applied to the case of Gaussian (quasifree) states of Bose systems, for which optimal measurements of the mean value are found.

Suggested Citation

  • Holevo, A. S., 1973. "Statistical decision theory for quantum systems," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 337-394, December.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:4:p:337-394
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    Cited by:

    1. Charles-Cadogan, G., 2021. "Utility Representation in Abstract Wiener Space," CRETA Online Discussion Paper Series 70, Centre for Research in Economic Theory and its Applications CRETA.
    2. René Schwonnek & David Reeb & Reinhard F. Werner, 2016. "Measurement Uncertainty for Finite Quantum Observables," Mathematics, MDPI, vol. 4(2), pages 1-21, June.
    3. Artur Czerwinski, 2022. "Quantum Communication with Polarization-Encoded Qubits under Majorization Monotone Dynamics," Mathematics, MDPI, vol. 10(21), pages 1-17, October.

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