Geodesic
Generalized uncertainty relations and efficient measurements in quantum systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 26 (1976) no. 3, pp. 316-329

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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. 
@article{TMF_1976_26_3_a3,
     author = {V. P. Belavkin},
     title = {Generalized uncertainty relations and efficient measurements in quantum systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {316--329},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_26_3_a3/}
}
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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/