A fully quantum asymptotic equipartition property

  • Authors:
  • Marco Tomamichel;Roger Colbeck;Renato Renner

  • Affiliations:
  • Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland;Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland and Institute of Theoretical Computer Science, ETH Zurich, Zurich, Switzerland;Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

The classical asymptotic equipartition property is the statement that, in the limit of a large number of identical repetitions of a random experiment, the output sequence is virtually certain to come from the typical set, each member of which is almost equally likely. In this paper, a fully quantum generalization of this property is shown, where both the output of the experiment sand side information are quantum. An explicit bound on the convergence is given, which is independent of the dimensionality of the side information. This naturally leads to a family of Rényi-like quantum conditional entropies, for which the von Neumann entropy emerges as a special case.