Details

Autor(en) / Beteiligte

• Wilde, Mark M.
• Winter, Andreas
• Yang, Dong

Titel

Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy

Ist Teil von

• Communications in mathematical physics, 2014, Vol.331 (2), p.593-622

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2014

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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” Rényi 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.