dorsal/arxiv
View SchemaCovariance and Fisher information in quantum mechanics
| Authors | Denes Petz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106125 |
| URL | https://arxiv.org/abs/quant-ph/0106125 |
| DOI | 10.1088/0305-4470/35/4/305 |
| Journal | J. Phys. A: Math. Gen. 35, 929-939 (2002) |
Abstract
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasis that Fisher informations are obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.
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"abstract": "Variance and Fisher information are ingredients of the Cramer-Rao inequality.\nWe regard Fisher information as a Riemannian metric on a quantum statistical\nmanifold and choose monotonicity under coarse graining as the fundamental\nproperty of variance and Fisher information. In this approach we show that\nthere is a kind of dual one-to-one correspondence between the candidates of the\ntwo concepts. We emphasis that Fisher informations are obtained from relative\nentropies as contrast functions on the state space and argue that the scalar\ncurvature might be interpreted as an uncertainty density on a statistical\nmanifold.",
"arxiv_id": "quant-ph/0106125",
"authors": [
"Denes Petz"
],
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"quant-ph"
],
"doi": "10.1088/0305-4470/35/4/305",
"journal_ref": "J. Phys. A: Math. Gen. 35, 929-939 (2002)",
"title": "Covariance and Fisher information in quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0106125"
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