|
| related topics |
| {information, entropy, channel} |
| {let, theorem, proof} |
| {state, states, entangled} |
| {states, state, optimal} |
| {observables, space, algebra} |
|
On the structure of optimal sets for tensor product channel
M. E. Shirokov
abstract: For a given quantum channel we consider two optimal sets of states, related
to the Holevo capacity and to the minimal output entropy of this channel. Some
properties of these sets as well as the necessary and sufficient condition for
their coincidence are obtained. The relations between additivity properties for
two quantum channels and the structure of the optimal sets for tensor product
of these channels are considered. It turns out that these additivity properties
are connected with the special hereditary property of the optimal sets for
tensor product channel. We explore the structural properties of these optimal
sets under two different assumptions.
The first assumption means that for tensor product of two channels with
arbitrary constraints there exists optimal ensemble with the product state
average. It turns out that exactly this assumption guarantees hereditary
property of the both optimal sets for tensor product channel and provides some
observations concerning the additivity problems.
The second assumption means additivity of the Holevo capacity for two
channels with arbitrary constraints. It turns out that exactly this assumption
guarantees strong hereditary property of the both optimal sets for tensor
product channel and provides the natural "projective" relations between these
sets and the optimal sets for single channels.
- oai_identifier:
- oai:arXiv.org:quant-ph/0402178
- categories:
- quant-ph
- comments:
- 25 pages
- arxiv_id:
- quant-ph/0402178
- journal_ref:
- Problems of Information Transmission, Vol. 42, No. 4, (2006),
23--40
- created:
- 2004-02-24
- updated:
- 2005-06-28
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