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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
Bosonic quantum error correction codes in superconducting quantum circuits
TL;DR: The recent progress of the bosonic codes, including the Gottesman-Kitaev-Preskill codes, cat codes, and binomial codes, are reviewed and the opportunities of bosony codes in various quantum applications are discussed, ranging from fault-tolerant quantum computation to quantum metrology.
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Quantum parameter estimation with optimal control
Jing Liu,Haidong Yuan +1 more
TL;DR: By exploring the additional degree of freedom offered by the controls higher precision limit can be achieved, and it is shown that the precision limit under the controlled schemes can go beyond the constraints put by the coherent time.
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Asymptotic performance of optimal state estimation in qubit system
Masahito Hayashi,Keiji Matsumoto +1 more
TL;DR: An asymptotic bound for the error of state estimation is derived when the quantum correlation is allowed to use in the measuring apparatus and it is proven that this bound can be achieved in any statistical model in the qubit system.
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Enhancing teleportation of quantum Fisher information by partial measurements
TL;DR: In this article, the authors proposed two schemes to enhance quantum Fisher information (QFI) teleportation under amplitude damping noise with the technique of partial measurements, and they showed that post-partial measurement can greatly enhance the teleported QFI, while the combination of prior partial measurement and postpartial measurement reversal could completely eliminate the effect of decoherence.
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Multiplied-Poisson noise in pulse, particle, and photon detection
TL;DR: In this paper, the authors examined the properties and applications of a point process that arises when each event of a primary Poisson process generates a random number of subsidiary events, with a given time course.
References
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Journal ArticleDOI
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.