36,640 research outputs found
Classical information capacity of a class of quantum channels
We consider the additivity of the minimal output entropy and the classical
information capacity of a class of quantum channels. For this class of channels
the norm of the output is maximized for the output being a normalized
projection. We prove the additivity of the minimal output Renyi entropies with
entropic parameters contained in [0, 2], generalizing an argument by Alicki and
Fannes, and present a number of examples in detail. In order to relate these
results to the classical information capacity, we introduce a weak form of
covariance of a channel. We then identify several instances of weakly covariant
channels for which we can infer the additivity of the classical information
capacity. Both additivity results apply to the case of an arbitrary number of
different channels. Finally, we relate the obtained results to instances of
bi-partite quantum states for which the entanglement cost can be calculated.Comment: 14 pages, RevTeX (replaced with published version
Ergodic Classical-Quantum Channels: Structure and Coding Theorems
We consider ergodic causal classical-quantum channels (cq-channels) which
additionally have a decaying input memory. In the first part we develop some
structural properties of ergodic cq-channels and provide equivalent conditions
for ergodicity. In the second part we prove the coding theorem with weak
converse for causal ergodic cq-channels with decaying input memory. Our proof
is based on the possibility to introduce joint input-output state for the
cq-channels and an application of the Shannon-McMillan theorem for ergodic
quantum states. In the last part of the paper it is shown how this result
implies coding theorem for the classical capacity of a class of causal ergodic
quantum channels.Comment: 19 pages, no figures. Final versio
Multiaccess quantum communication and product higher rank numerical range
In the present paper we initiate the study of the product higher rank
numerical range. The latter, being a variant of the higher rank numerical range
[M.--D. Choi {\it et al.}, Rep. Math. Phys. {\bf 58}, 77 (2006); Lin. Alg.
Appl. {\bf 418}, 828 (2006)], is a natural tool for studying construction of
quantum error correction codes for multiple access channels. We review
properties of this set and relate it to other numerical ranges, which were
recently introduced in the literature. Further, the concept is applied to the
construction of codes for bi--unitary two--access channels with a hermitian
noise model. Analytical techniques for both outerbounding the product higher
rank numerical range and determining its exact shape are developed for this
case. Finally, the reverse problem of constructing a noise model for a given
product range is considered.Comment: 26 pages, 6 figure
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