A Fully Quantum Asymptotic Equipartition Property

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 2009-12, Vol.55 (12), p.5840-5847
Main Authors: Tomamichel, M., Colbeck, R., Renner, R.
Format: Article
Language:English
Subjects:
Access methods and protocols, osi model
Applied sciences
Asymptotic equipartition property
Asymptotic methods
Asymptotic properties
Classical and quantum physics: mechanics and fields
Computer science
Convergence
Entropy
Exact sciences and technology
Information processing
Information theory
Information, signal and communications theory
Physics
Probability distribution
Quantum entanglement
Quantum information
Quantum mechanics
Random variables
Repetition
RÉnyi entropies
smooth entropies
Telecommunications
Telecommunications and information theory
Teleprocessing networks. Isdn
von Neumann entropy
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Summary: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 and 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 REacutenyi-like quantum conditional entropies, for which the von Neumann entropy emerges as a special case.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2009.2032797