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Quantum detection and estimation theory
TLDR
In this article, 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, and a quantum counterpart of the Cramer-Rao inequality of conventional statistics sets a lower bound to the mean-square errors of such estimates.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 Cramer-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.read more
Citations
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Journal ArticleDOI
Process positive-operator-valued measure: A mathematical framework for the description of process tomography experiments
TL;DR: In this paper, the authors introduce a mathematical framework for the description of measurements of quantum processes, which can be treated in a similar way as state estimation problems, only replacing the concept of positive-operator-valued measure (POVM) by the process POVM (PPOVM).
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Minimum-error discrimination between symmetric mixed quantum states
Chih-Lung Chou,Li-Yi Hsu +1 more
TL;DR: In this paper, a solution of finding an optimal measurement strategy for distinguishing between symmetric mixed quantum states is provided. But it is assumed that the matrix elements of at least one of the symmetric quantum states are all real and non-negative in the basis of the eigenstates of the symmetry operator.
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Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
TL;DR: It is rigorously proved that the fidelity susceptibility is proportional to the quantum Fisher information, and this proportional relation is generally established for density matrices with arbitrary ranks.
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Ultimate Data Hiding in Quantum Mechanics and Beyond
TL;DR: The main result of the paper is the determination of the maximal data hiding ratio obtainable in an arbitrary GPT, which is shown to scale linearly in the minimum of the local dimensions.
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Comparison Between the Cramer-Rao and the Mini-max Approaches in Quantum Channel Estimation
TL;DR: It is shown that the local asymptotic mini-max bound is strictly larger than the Cramér-Rao bound in the phase estimation case while both bounds coincide when the minimum mean square error decreases with the order of O(\frac{1}{n}) .
References
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Coherent and incoherent states of the radiation field
TL;DR: In this article, the photon statistics of arbitrary fields in fully quantum-mechanical terms are discussed, and a general method of representing the density operator for the field is discussed as well as a simple formulation of a superposition law for photon fields.
Book
Detection, Estimation, And Modulation Theory
TL;DR: Detection, estimation, and modulation theory, Detection, estimation and modulation theorists, اطلاعات رسانی کشاورزی .
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Description of States in Quantum Mechanics by Density Matrix and Operator Techniques
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On the problems of the most efficient tests of statistical hypotheses.
J. Neyman,E. S. Pearson +1 more
TL;DR: The problem of testing statistical hypotheses is an old one as discussed by the authors, and its origin is usually connected with the name of Thomas Bayes, who gave the well-known theorem on the probabilities a posteriori of the possible causes of a given event.