A Fully Quantum Asymptotic Equipartition Property

Authors:
  • MTMarco Tomamichel
    Marco Tomamichel
  • RCRoger Colbeck
    Roger Colbeck
  • RRRenato Renner
    Renato Renner
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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 equally likely. In this paper, we prove a fully quantum generalization of this property, where both the output of the experiment and side information are quantum. This naturally leads to a family of Renyi-like quantum conditional entropies, for which the von Neumann entropy emerges as a special case.