PIRSA:10070019 Conference

DOI10.48660/10070019

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

Szarek, S. (2010). Hastings' additivity counterexample and a sharp version of Dvoretzky theorem. Perimeter Institute. https://pirsa.org/10070019

Szarek, Stanislaw. Hastings' additivity counterexample and a sharp version of Dvoretzky theorem. Perimeter Institute, Jul. 06, 2010, https://pirsa.org/10070019 

@misc{ pirsa_PIRSA:10070019,
  doi = {10.48660/10070019},
  url = {https://pirsa.org/10070019},
  author = {Szarek, Stanislaw},
  keywords = {},
  language = {en},
  title = {Hastings{\textquoteright} additivity counterexample and a sharp version of Dvoretzky theorem},
  publisher = {Perimeter Institute},
  year = {2010},
  month = {jul},
  note = {PIRSA:10070019 see, \url{https://pirsa.org}}
}

Abstract

In this talk we will explain how the main step technical steps in the proofs by Hastings and Hayden-Winter of the non-additivity of the minimal output von Neumann and $p$-Renyi entropy (for any $p>1$) can be reduced to a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies. This substantially simplifies their analysis, at least on the conceptual level, and provides an alternative point of view on these and related questions. Joint work with G. Aubrun and E. Werner

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