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Comments on Hastings’ Additivity Counterexamples

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Davis, CA, USA

    Motohisa Fukuda

  2. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Christopher King

  3. Department of Physics, Northeastern University, Boston, MA, 02115, USA

    David K. Moser

Authors
  1. Motohisa Fukuda
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  2. Christopher King
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  3. David K. Moser
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Correspondence to Christopher King.

Additional information

Communicated by M.B. Ruskai

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Fukuda, M., King, C. & Moser, D.K. Comments on Hastings’ Additivity Counterexamples. Commun. Math. Phys. 296, 111–143 (2010). https://doi.org/10.1007/s00220-010-0996-9

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  • DOI: https://doi.org/10.1007/s00220-010-0996-9

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