The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory

  • Mario Berta
  • Matthias Christandl
  • Renato Renner
Open Access


The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel’s entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.


Entangle State Quantum Channel Classical Communication Local Operation Trace Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Jürg Wullschleger and Andreas Winter for inspiring discussions and William Matthews and Debbie Leung for detailed feedback on the first version of this paper as well as for suggesting Figs. 2 and 4. MB and MC are supported by the Swiss National Science Foundation (grant PP00P2-128455) and the German Science Foundation (grants CH 843/1-1 and CH 843/2-1). RR acknowledges support from the Swiss National Science Foundation (grant No. 200021-119868). Part of this work was carried out while MB and MC were affiliated with the Faculty of Physics at the University of Munich in Germany.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Mario Berta
    • 1
  • Matthias Christandl
    • 1
  • Renato Renner
    • 1
  1. 1.Institute for Theoretical PhysicsETH ZurichZurichSwitzerland

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