Physics – Quantum Physics
Scientific paper
2004-12-03
Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp. 316--329, Plenum, 1976
Physics
Quantum Physics
17 pages. Translated from Russian and typeset in LaTeX from Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp. 3
Scientific paper
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this inequality leads to a precise formulation of a generalized uncertainty principle for arbitrary states, in contrast to Helstrom's symmetric variant in which these relations are obtained only for pure states. A notion of canonical states is introduced and the lower mean square error bound is found for estimating of the parameters of canonical states, 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 efficient measurements or quasimeasurements.
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