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
Distributed quantum sensing enhanced by continuous-variable error correction
TL;DR: It is shown that using continuous-variable error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of $M$.
Journal ArticleDOI
Quantum retrodiction in open systems
TL;DR: In this article, a general master equation for the backward time evolution of the measured state, which can be used for calculating preparation probabilities, is proposed for the driven two-level atom coupled to the electromagnetic field.
Journal ArticleDOI
Joint measurements of spin, operational locality, and uncertainty
TL;DR: In this paper, a spin-1/2 particle was measured along any two directions, and it was shown how to obtain a bound on how sharp the joint measurement can be.
Journal ArticleDOI
Optimal detection of losses by thermal probes
TL;DR: In this paper, the authors consider the case when one of the values for the loss parameter is zero, i.e., the detection of a possible loss against the alternative hypothesis of an ideal lossless channel is performed by inputting one- or two-mode squeezed thermal states with fixed total energy.
Journal ArticleDOI
Minimax and adaptive estimation of the Wigner function in quantum homodyne tomography with noisy data
TL;DR: In this article, the authors estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems, represented through the Wigner function, a generalized probability density on ℝ2 which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics.
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.