PIRSA:10070020 Conference

DOI10.48660/10070020

Conference/School: Random Matrix Techniques in Quantum Information - 2010

Brandao, F. (2010). Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration. Perimeter Institute. https://pirsa.org/10070020

Brandao, Fernando. Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration. Perimeter Institute, Jul. 06, 2010, https://pirsa.org/10070020 

@misc{ pirsa_PIRSA:10070020,
  doi = {10.48660/10070020},
  url = {https://pirsa.org/10070020},
  author = {Brandao, Fernando},
  keywords = {},
  language = {en},
  title = {Hasting{\textquoteright}s counterexamples on the minimum output entropy additivity conjecture by measure concentration},
  publisher = {Perimeter Institute},
  year = {2010},
  month = {jul},
  note = {PIRSA:10070020 see, \url{https://pirsa.org}}
}

Abstract

In 2008 Hastings reported a randomized construction of channels violating the minimum output entropy additivity conjecture. In this talk we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. We prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension.

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