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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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Optimal quantum detectors for unambiguous detection of mixed states
TL;DR: In this article, the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states was considered and necessary and sufficient conditions for an optimal measurement that minimizes the probability of an inconclusive result were derived.
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Experimental simulation of closed timelike curves
TL;DR: This work experimentally simulate the nonlinear behaviour of a qubit interacting unitarily with an older version of itself, addressing some of the fascinating effects that arise in systems traversing a closed timelike curve.
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Private database queries using one quantum state
TL;DR: It is proved that the proposed protocol is secure in terms of the user security and the database security and can be implemented in the situation where not all the parties can afford expensive quantum resources and operations.
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An estimation theoretical characterization of coherent states
Akio Fujiwara,Hiroshi Nagaoka +1 more
TL;DR: In this paper, the authors introduce a class of quantum pure state models called the coherent models, which is an even-dimensional manifold of pure states whose tangent space is characterized by a symplectic structure.
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Measurement does not always aid state discrimination
TL;DR: In this article, the problem of discriminating between nonorthogonal quantum states with the least probability of error was investigated, and the best strategy for some sets of states is to make no measurement at all and simply to always assign the most commonly occurring state.
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.