Communications in Mathematical Physics

, Volume 338, Issue 1, pp 103–137 | Cite as

Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels

  • Marco TomamichelEmail author
  • Vincent Y. F. Tan


We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible. In this work we consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels. In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity. The behavior is governed by a new channel parameter, called channel dispersion, for which we provide a geometrical interpretation.


Quantum Channel Relative Entropy Direct Part Divergence Radius Channel Image 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of PhysicsThe University of SydneySydneyAustralia
  2. 2.Centre for Quantum TechnologiesUniversity of SingaporeSingaporeSingapore
  3. 3.Department of Electrical and Computer EngineeringUniversity of SingaporeSingaporeSingapore
  4. 4.Department of MathematicsUniversity of SingaporeSingaporeSingapore

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