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TMF, 1976, Volume 26, Number 3, Pages 316–329 (Mi tmf3225)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalized uncertainty relations and efficient measurements in quantum systems

V. P. Belavkin


Abstract: We consider two variants of a quantum-statistical generalization of the Cramer–Rao inequality that establish an invariant lower bound on the mean square error of a generalized quantum measurement. In contrast to Helstrom's variant [1], the proposed complex variant of this inequality leads to a precise formulation of a generalized uncertainty principle for arbitrary states. A bound is found for the accuracy of estimating the parameters of canonical states and, in particular, the canonical parameters of a Lie group. It is shown that these bounds are globally attainable only for canonical states for which there exist effficient measurements and quasimeasurements.

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English version:
Theoretical and Mathematical Physics, 1976, 26:3, 213–222

Bibliographic databases:

Received: 20.06.1975

Citation: V. P. Belavkin, “Generalized uncertainty relations and efficient measurements in quantum systems”, TMF, 26:3 (1976), 316–329; Theoret. and Math. Phys., 26:3 (1976), 213–222

Citation in format AMSBIB
\Bibitem{Bel76}
\by V.~P.~Belavkin
\paper Generalized uncertainty relations and efficient measurements in quantum systems
\jour TMF
\yr 1976
\vol 26
\issue 3
\pages 316--329
\mathnet{http://mi.mathnet.ru/tmf3225}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=449358}
\transl
\jour Theoret. and Math. Phys.
\yr 1976
\vol 26
\issue 3
\pages 213--222
\crossref{https://doi.org/10.1007/BF01032091}


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  • http://mi.mathnet.ru/eng/tmf/v26/i3/p316

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Theory Probab. Appl., 53:2 (2009), 329–334  mathnet  crossref  crossref  zmath  isi
    2. Luati A., “An Approximate Quantum Cramer-Rao Bound Based on Skew Information”, Bernoulli, 17:2 (2011), 628–642  crossref  isi
    3. Hayashi M., “Quantum Information Theory Mathematical Foundation Second Edition Prologue”: Hayashi, M, Quantum Information Theory: Mathematical Foundation, 2Nd Edition, Graduate Texts in Physics, Springer-Verlag Berlin, 2017, XXXV–XLIII  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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