A Fully Quantum Asymptotic Equipartition Property

Details A Fully Quantum Asymptotic Equipartition Property A Fully Quantum Asymptotic Equipartition Property

2008-11-10

arxiv.org/abs/0811.1221v3

IEEE Trans. on Inf. Theory 55 (2009) p. 5840-5847

Physics

Quantum Physics

Main claim is updated with improved bounds

Scientific paper

10.1109/TIT.2009.2032797

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, we prove a fully quantum generalization of this property, where both the output of the experiment and side information are quantum. We give an explicit bound on the convergence, which is independent of the dimensionality of the side information. This naturally leads to a family of Renyi-like quantum conditional entropies, for which the von Neumann entropy emerges as a special case.

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