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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
Fundamental Quantum Limits to Waveform Detection
Mankei Tsang,Ranjith Nair +1 more
TL;DR: In this article, lower error bounds for waveform detection via a quantum system have been shown, and analytic expressions for the bounds in some cases of interest and discuss how the limits can be approached using quantum control techniques.
Proceedings ArticleDOI
A lower bound on the probability of error in quantum state discrimination
TL;DR: A lower bound on the probability of error in quantum state discrimination is given, which is a weighted sum of the pairwise fidelities of the states to be distinguished.
Journal ArticleDOI
Continuous quantum hypothesis testing.
TL;DR: A general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations, useful for quantum detection and experimental tests of quantum mechanics in general.
Journal ArticleDOI
Optimal Quantum Tomography
TL;DR: In this paper, a short review article illustrates the latest theoretical developments on quantum tomography, regarding general optimization methods for both data processing and setup, the basic theoretical tool is the informationally complete measurement, the optimization theory for the setup is based on the new theoretical approach of quantum combs.
Journal ArticleDOI
Dissipative quantum metrology in manybody systems of identical particles
TL;DR: In this article, a dissipative (open) quantum system of identical particles is considered, in which a parameter of the open dynamics itself is to be estimated, and the entanglement produced in the course of the dissipative dynamics may help the estimation task.
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 .
Journal ArticleDOI
Description of States in Quantum Mechanics by Density Matrix and Operator Techniques
Journal ArticleDOI
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.