Open AccessBook
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
More filters
Journal ArticleDOI
Ultimate Precision Bound of Quantum and Subwavelength Imaging.
TL;DR: The ultimate precision bound for resolving two pointlike sources in an arbitrary quantum state is established, with a simple formula for the specific case of two thermal sources, finding that quantum-correlated sources can be superresolved at the sub-Rayleigh scale.
Journal ArticleDOI
Wigner-Yanase skew information vs. quantum Fisher information
TL;DR: The Wigner-Yanase skew information and the quantum Fisher information defined via symmetric logarithmic derivatives are natural generalizations of the classical Fisher information and are comparable.
Journal ArticleDOI
Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination
TL;DR: A quantum receiver based on a novel adaptive measurement scheme and a high-bandwidth, high-detection-efficiency system for single-photon counting and an unconditionally discriminates between four nonorthogonal coherent states is presented.
Journal ArticleDOI
Quantum Fisher information of the Greenberger-Horne-Zeilinger state in decoherence channels
TL;DR: In this paper, the quantum Fisher information of a state with respect to SU(2) rotations under three decoherence channels: the amplitude-damping, phase-ding, and depolarizing channels is analyzed analytically.
Journal ArticleDOI
Quantum inference of states and processes
TL;DR: In this paper, the maximum-likelihood principle is used to unify inference of quantum states and processes from experimental noisy data, and a generic quantum process may be estimated simultaneously with unknown quantum probe states, provided that measurements on probe and transformed probe states are available.
References
More filters
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.