Geodesic
Generalized uncertainty relations and efficient measurements in quantum systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 26 (1976) no. 3, pp. 316-329 
V. P. Belavkin. Generalized uncertainty relations and efficient measurements in quantum systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 26 (1976) no. 3, pp. 316-329. http://geodesic.mathdoc.fr/item/TMF_1976_26_3_a3/
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     title = {Generalized uncertainty relations and efficient measurements in quantum systems},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] C. W. Helstrom, Phys. Lett., 25A (1967), 101 | DOI

[2] V. P. Belavkin, Zarubezhnaya radioelektronika, 5 (1975), 3 | MR

[3] V. P. Belavkin, Kand. diss., MGU, 1972

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[6] V. P. Belavkin, Stochastics, 1 (1975), 315 | DOI | MR | Zbl

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[12] G. A. Zaitsev, Algebraicheskie problemy matematicheskoi fiziki, «Nauka», 1974 | MR