dorsal/arxiv
View SchemaSufficiency in quantum statistical inference. A survey with examples
| Authors | Anna Jencova, Denes Petz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604091 |
| URL | https://arxiv.org/abs/quant-ph/0604091 |
| Journal | J. Infinite Dimensional Analysis and Quantum Probability, 9(2006), 331-352. |
Abstract
This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated paralelly to the the measure theoretic case. It turns out that several classical examples and results have a non-commutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result.
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"abstract": "This paper attempts to give an overview about sufficiency in the setting of\nquantum statistics. The basic concepts are treated paralelly to the the measure\ntheoretic case. It turns out that several classical examples and results have a\nnon-commutative analogue. Some of the results are presented without proof (but\nwith exact references) and the presentation is intended to be self-contained.\nThe main examples discussed in the paper are related the Weyl algebra and to\nthe exponential family of states. The characterization of sufficiency in terms\nof quantum Fisher information is a new result.",
"arxiv_id": "quant-ph/0604091",
"authors": [
"Anna Jencova",
"Denes Petz"
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],
"journal_ref": "J. Infinite Dimensional Analysis and Quantum Probability, 9(2006),\n 331-352.",
"title": "Sufficiency in quantum statistical inference. A survey with examples",
"url": "https://arxiv.org/abs/quant-ph/0604091"
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