Strong Converse Rates for Quantum Communication

Marco Tomamichel, Mark M. Wilde, Andreas Winter

Research output: Contribution to journalArticleResearchpeer-review

38 Citations (Scopus)


© 1963-2012 IEEE. We revisit a fundamental open problem in quantum information theory, namely, whether it is possible to transmit quantum information at a rate exceeding the channel capacity if we allow for a non-vanishing probability of decoding error. Here, we establish that the Rains information of any quantum channel is a strong converse rate for quantum communication. For any sequence of codes with rate exceeding the Rains information of the channel, we show that the fidelity vanishes exponentially fast as the number of channel uses increases. This remains true even if we consider codes that perform classical postprocessing on the transmitted quantum data. As an application of this result, for generalized dephasing channels, we show that the Rains information is also achievable, and thereby establish the strong converse property for quantum communication over such channels. Thus, we conclusively settle the strong converse question for a class of quantum channels that have a non-trivial quantum capacity.
Original languageEnglish
Article number7586115
Pages (from-to)715-727
JournalIEEE Transactions on Information Theory
Issue number1
Publication statusPublished - 1 Jan 2017


  • generalized dephasing channels
  • quantum communication
  • Rains relative entropy
  • strong converse


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