dorsal/arxiv
View SchemaA quantum version of Sanov's theorem
| Authors | I. Bjelakovic, J. -D. Deuschel, T. Krueger, R. Seiler, Ra. Siegmund-Schultze, A. Szkola |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412157 |
| URL | https://arxiv.org/abs/quant-ph/0412157 |
| DOI | 10.1007/s00220-005-1426-2 |
Abstract
We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\Psi$ of stationary quantum product states asymptotically separating them from another fixed stationary product state. Analogously to the classical case, the exponential separating rate is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set $\Psi$. However, while in the classical case the separating subsets can be chosen universal, in the sense that they depend only on the chosen set of i.i.d. processes, in the quantum case the choice of the separating subspaces depends additionally on the reference state.
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"abstract": "We present a quantum extension of a version of Sanov\u0027s theorem focussing on a\nhypothesis testing aspect of the theorem: There exists a sequence of typical\nsubspaces for a given set $\\Psi$ of stationary quantum product states\nasymptotically separating them from another fixed stationary product state.\nAnalogously to the classical case, the exponential separating rate is equal to\nthe infimum of the quantum relative entropy with respect to the quantum\nreference state over the set $\\Psi$. However, while in the classical case the\nseparating subsets can be chosen universal, in the sense that they depend only\non the chosen set of i.i.d. processes, in the quantum case the choice of the\nseparating subspaces depends additionally on the reference state.",
"arxiv_id": "quant-ph/0412157",
"authors": [
"I. Bjelakovic",
"J. -D. Deuschel",
"T. Krueger",
"R. Seiler",
"Ra. Siegmund-Schultze",
"A. Szkola"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"math.PR"
],
"doi": "10.1007/s00220-005-1426-2",
"title": "A quantum version of Sanov\u0027s theorem",
"url": "https://arxiv.org/abs/quant-ph/0412157"
},
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