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Cramér-Rao inequalities for operator-valued measures in quantum mechanics

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Abstract

The theory of estimation of parameters of quantum-mechanical density operators is expressed in terms of the measurement of operator-valued measures. Lower bounds on mean-square errors of parameter estimates are set by two quantum-mechanical forms of the Cramér-Rao inequality of classical statistics, derived here in terms of such measures. The results are exemplified by the simultaneous estimation of the real and imaginary parts of the complex amplitude of a coherent oscillation in the presence of thermal noise.

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Authors and Affiliations

  1. Department of Applied Physics and Information Science, University of California, San Diego

    Carl W. Helstrom

  2. Department of Applied Physics and Information Science, University of California, 92037, La Jolla, California

    Carl W. Helstrom

Authors
  1. Carl W. Helstrom
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This research was supported by grant NSF GK-33811 from the National Science Foundation.

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Helstrom, C.W. Cramér-Rao inequalities for operator-valued measures in quantum mechanics. Int J Theor Phys 8, 361–376 (1973). https://doi.org/10.1007/BF00687093

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  • DOI: https://doi.org/10.1007/BF00687093

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