Communications in Mathematical Physics

, Volume 355, Issue 3, pp 1283–1315 | Cite as

Moderate Deviation Analysis for Classical Communication over Quantum Channels

  • Christopher T. ChubbEmail author
  • Vincent Y. F. Tan
  • Marco Tomamichel


We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by Altŭg and Wagner as well as Polyanskiy and Verdú. We derive such a tradeoff for classical-quantum (as well as image-additive) channels in terms of the channel capacity and the channel dispersion, giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data. To derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime. Due to the central importance of the latter task, we expect that our techniques will find further applications in the analysis of other quantum information processing tasks.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Christopher T. Chubb
    • 1
    Email author
  • Vincent Y. F. Tan
    • 2
    • 3
  • Marco Tomamichel
    • 1
    • 4
  1. 1.Centre for Engineered Quantum Systems, School of PhysicsUniversity of SydneySydneyAustralia
  2. 2.Department of Electrical and Computer EngineeringNational University of SingaporeSingaporeSingapore
  3. 3.Department of MathematicsNational University of SingaporeSingaporeSingapore
  4. 4.Centre for Quantum Software and InformationUniversity of Technology SydneySydneyAustralia

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