Quantum detection and estimation theory

Abstract

A review. Quantum detection theory is a reformulation, in quantum-mechanical terms, of statistical decision theory as applied to the detection of signals in random noise. Density operators take the place of the probability density functions of conventional statistics. The optimum procedure for choosing between two hypotheses, and an approximate procedure valid at small signal-to-noise ratios and called threshold detection, are presented. Quantum estimation theory seeks best estimators of parameters of a density operator. A quantum counterpart of the Cramér-Rao inequality of conventional statistics sets a lower bound to the mean-square errors of such estimates. Applications at present are primarily to the detection and estimation of signals of optical frequencies in the presence of thermal radiation.

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This paper was prepared under grant NGR-05-009-079 from the National Aeronautics and Space Administration.

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Helstrom, C.W. Quantum detection and estimation theory. J Stat Phys 1, 231–252 (1969). https://doi.org/10.1007/BF01007479

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Key words

  • signal detection
  • detection theory
  • parameter estimation
  • statistical estimation
  • estimation theory
  • quantum theory
  • decision theory
  • hypothesis testing
  • statistical decisions