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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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General Strategies for Discrimination of Quantum States
TL;DR: In this paper, the authors derived general discrimination of quantum states chosen from a certain set, given initial $M$ copies of each state, and obtained the matrix inequality, which describes the bound between the maximum probability of correctly determining and that of error.
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Coherence distillation machines are impossible in quantum thermodynamics.
TL;DR: In this article, it was shown that for general (full-rank) mixed states, it is possible to distill a sublinear number of pure coherent states with vanishing error.
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Explicit formula for the Holevo bound for two-parameter qubit estimation problem
TL;DR: In this paper, the Holevo bound for estimating any two-parameter family of qubit mixed-states in terms of quantum versions of Fisher information was derived, based on the symmetric logarithmic derivative (SLD), the right log-linear derivative (RLD) Fisher information, and a given weight matrix.
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Quantum-optimal detection of one-versus-two incoherent sources with arbitrary separation
TL;DR: In this paper, the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem is analyzed: deciding whether the optical field on the image plane is generated by one source or two weaker sources with arbitrary separation.
Posted Content
Resource theory of entanglement for bipartite quantum channels
TL;DR: In this article, the authors focus on the resource theory of entanglement for bipartite channels and establish several fundamental tasks and results regarding it, and establish bounds on several pertinent information processing tasks.
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
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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.