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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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Squeezed vacuum as a universal quantum probe
Roberto Gaiba,Matteo G. A. Paris +1 more
TL;DR: In this article, the authors evaluate the relevant quantum Fisher information (QFI) and derive the ultimate bound on precision, and find that single and two-mode squeezed vacuums represent an optimal and universal class of probe states, achieving the Heisenberg limit to precision in terms of the overall energy of the probe.
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Presumable solutions of quantum phase problem and their flaws
A Luks,V Perinova +1 more
TL;DR: A combination of less frequent criticism with positive investigations has resulted in the substitution of group theoretic considerations by a simpler quantum mechanical model, has taken into account homodyne and heterodyne detection schemes, and proceeded by an analysis of phase data processing.
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A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model
TL;DR: In this paper, a comparative study between LQFI and LQU was conducted for the quantum Heisenberg XY model and the isotropic XY model submitted to an external magnetic field and it was shown that LFI reveals more quantum correlations than LQU.
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Parity bit in quantum cryptography.
TL;DR: This paper finds the measurement which provides the optimal mutual information about the parity bit and calculates that information, and proves that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping.
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Attaining the Ultimate Precision Limit in Quantum State Estimation
Yuxiang Yang,Yuxiang Yang,Giulio Chiribella,Masahito Hayashi,Masahito Hayashi,Masahito Hayashi +5 more
TL;DR: In this article, the authors derived a bound on the precision of state estimation for finite dimensional quantum systems and proved its attainability in the generic case where the spectrum is non-degenerate.
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.