Generalized uncertainty relations and efficient measurements in quantum systems
| dc.creator | Belavkin, V. P. | |
| dc.date | 2004-12-03 | |
| dc.date.accessioned | 2026-07-07T06:11:41Z | |
| dc.date.available | 2026-07-07T06:11:41Z | |
| dc.description | 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. | |
| dc.description | 17 pages. Translated from Russian and typeset in LaTeX from Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp. 316--329, March, 1976 | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0412030 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0412030 | |
| dc.identifier | Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp. 316--329, Plenum, 1976 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92555 | |
| dc.subject | Quantum Physics | |
| dc.title | Generalized uncertainty relations and efficient measurements in quantum systems | |
| dc.type | text |