2013/06/30 by Mark M. Wilde, Andreas Winter, Dong Yang · 7 citations
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.IT #math-ph #math.IT #math.MP
paper · pdf · doi:10.1007/s00220-014-2122-x
published as Communications in Mathematical Physics, vol. 331, no. 2, pages 593-622, October 2014 · 33 pages; v4: minor changes throughout, accepted for publication in Communications in Mathematical Physics
arxiv created 2014/05/22 · arxiv updated 2014/07/31
A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel. Along with a corresponding achievability statement for rates below the capacity, such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication. Here, we show that such a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former). These results follow by bounding the success probability in terms of a "sandwiched" Renyi relative entropy, by showing that this quantity is subadditive for all entanglement-breaking and Hadamard channels, and by relating this quantity to the Holevo capacity. Prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results.