Constant compositions in the sphere packing bound for classical-quantum channels

Marco Dalai, Andreas Winter

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)


© 1963-2012 IEEE. The sphere packing bound, in the form given by Shannon, Gallager, and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the Lovász theta function. In this paper, we extend the study to the case of constant-composition codes. We first extend the sphere packing bound for classical-quantum channels to this case, and we then show that the obtained result is related to a variation of the Lovász theta function studied by Marton. We then propose a further extension to the case of varying channels and codewords with a constant conditional composition given a particular sequence. This extension is finally applied to auxiliary channels to deduce a bound, which is useful in the low rate region and which can be interpreted as an extension of the Elias bound.
Original languageEnglish
Article number7979569
Pages (from-to)5603-5617
JournalIEEE Transactions on Information Theory
Issue number9
Publication statusPublished - 1 Sep 2017


  • Quantum channels
  • constant composition codes
  • error exponents
  • sphere packing bound
  • zero-error capacity


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