Ergodic Classical-Quantum Channels: Structure and Coding Theorems
<|reference_start|>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.<|reference_end|>
@article{bjelakovic2006ergodic,
    title={Ergodic Classical-Quantum Channels: Structure and Coding Theorems},
    author={Igor Bjelakovic, Holger Boche},
    journal={IEEE Transactions on Information Theory Vol. 54, No. 2, pp.
  723-742, February 2008},
    year={2006},
    doi={10.1109/TIT.2007.913232},
    archivePrefix={arXiv},
    eprint={quant-ph/0609229},
    primaryClass={quant-ph cs.IT math-ph math.IT math.MP}
}