Arbitrarily Varying and Compound Classical-Quantum Channels and a Note on Quantum Zero-Error Capacities

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• 作者：Igor Bjelakovi? (18)
  Holger Boche (18)
  Gisbert Jan?en (18)
  Janis N?tzel (18)
  
• 关键词：arbitrarily varying classical ; quantum channels ; compound classical ; quantum channels ; zero error capacity ; Ahlswedes dichotomy ; weak converse ; strong converse
• 刊名：Lecture Notes in Computer Science
• 出版年：2013
• 出版时间：2013
• 年：2013
• 卷：7777
• 期：1
• 页码：284-297
• 全文大小：506KB
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• 作者单位：Igor Bjelakovi? (18)
  Holger Boche (18)
  Gisbert Jan?en (18)
  Janis N?tzel (18)
  
  18. Lehrstuhl für Theoretische Informationstechnik, Technische Universit?t München, 80290, München, Germany
  
• ISSN：1611-3349

文摘

We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error criterion to this statement is also established. We use this result together with the robustification and elimination technique developed by Ahlswede in order to give an alternative proof of the direct part of the coding theorem for a finite classical-quantum arbitrarily varying channels with the criterion of success being average error probability. Moreover we provide a proof of the strong converse to the random coding capacity in this setting. The notion of symmetrizability for the maximal error probability is defined and it is shown to be both necessary and sufficient for the capacity for message transmission with maximal error probability criterion to equal zero. Finally, it is shown that the connection between zero-error capacity and certain arbitrarily varying channels is, just like in the case of quantum channels, only partially valid for classical-quantum channels.