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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
Distinguishing between optical coherent states with imperfect detection
TL;DR: In this article, the effects of detector dark counts, dead time, signal processing bandwidth and phase noise in the communication channel were analyzed under a physically realistic model of photodetection.
Book
Quantum Theory from First Principles: An Informational Approach
TL;DR: In this article, the authors reconstruct quantum theory from six information-theoretical principles, by rebuilding the quantum rules from the bottom up, using intuitive graphical notation to represent equations, and with shorter and more efficient derivations.
Journal ArticleDOI
Symmetry Principles in Quantum Systems Theory
TL;DR: In this paper, a complete lattice of irreducible simple subalgebras of su(2^n) for up to n=15 qubits is given, which complements the symmetry condition by allowing for easy tests solving homogeneous linear equations.
Journal ArticleDOI
Exact uncertainty relations
TL;DR: The Heisenberg inequality can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions as mentioned in this paper, and the statistics of complementary observables are connected by an ''exact'' uncertainty relation.
Proceedings ArticleDOI
Quantum algorithm for a generalized hidden shift problem
Andrew M. Childs,Wim van Dam +1 more
TL;DR: For any fixed positive ε, an efficient quantum algorithm is given for the generalized hidden shift problem, based on the "pretty good measurement" and uses H. Lenstra's (classical) algorithm for integer programming as a subroutine.
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.