Communications in Mathematical Physics

, Volume 296, Issue 1, pp 111–143 | Cite as

Comments on Hastings’ Additivity Counterexamples

  • Motohisa Fukuda
  • Christopher King
  • David K. Moser


Hastings [12] recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings’ proof. In addition to a careful elucidation of the details of the proof, we also present bounds for the minimal dimensions needed to obtain a counterexample.


Quantum Channel Input State Random State Partial Isometry Output Entropy 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Motohisa Fukuda
    • 1
  • Christopher King
    • 2
  • David K. Moser
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA
  3. 3.Department of PhysicsNortheastern UniversityBostonUSA

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