Communications in Mathematical Physics

, Volume 331, Issue 2, pp 593–622 | Cite as

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



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.


Success Probability Quantum Channel Density Operator Relative Entropy Quantum Operation 


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical PhysicsLouisiana State UniversityBaton RougeUSA
  2. 2.ICREA, Informació i Fenomens, QuànticsUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  3. 3.Física Teòrica, Informació i Fenomens, QuànticsUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  4. 4.School of MathematicsUniversity of BristolBristolUK
  5. 5.Laboratory for Quantum InformationChina Jiliang UniversityHangzhouChina

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