This article is cited in 44 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.

Received: 20.06.1975

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

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