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| related topics |
| {information, entropy, channel} |
| {let, theorem, proof} |
| {observables, space, algebra} |
| {classical, space, random} |
| {key, protocol, security} |
| {cos, sin, state} |
|
A quantum version of Sanov's theorem
I. Bjelakovic, J. -D. Deuschel, T. Krueger, R. Seiler, Ra. Siegmund-Schultze, A. Szkola
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0412157
- categories:
- quant-ph math-ph math.MP math.PR
- comments:
- 15 pages
- arxiv_id:
- quant-ph/0412157
- created:
- 2004-12-20
Full article ▸
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