dorsal/arxiv
View SchemaGeneralized uncertainty relations and efficient measurements in quantum systems
| Authors | V. P. Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412030 |
| URL | https://arxiv.org/abs/quant-ph/0412030 |
| Journal | Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp. 316--329, Plenum, 1976 |
Abstract
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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"abstract": "We consider two variants of a quantum-statistical generalization of the\nCramer-Rao inequality that establishes an invariant lower bound on the mean\nsquare error of a generalized quantum measurement. The proposed complex variant\nof this inequality leads to a precise formulation of a generalized uncertainty\nprinciple for arbitrary states, in contrast to Helstrom\u0027s symmetric variant in\nwhich these relations are obtained only for pure states. A notion of canonical\nstates is introduced and the lower mean square error bound is found for\nestimating of the parameters of canonical states, in particular, the canonical\nparameters of a Lie group. It is shown that these bounds are globally\nattainable only for canonical states for which there exist efficient\nmeasurements or quasimeasurements.",
"arxiv_id": "quant-ph/0412030",
"authors": [
"V. P. Belavkin"
],
"categories": [
"quant-ph"
],
"journal_ref": "Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp.\n 316--329, Plenum, 1976",
"title": "Generalized uncertainty relations and efficient measurements in quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0412030"
},
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