2008

A Fully Quantum Asymptotic Equipartition Property

Tomamichel, Marco, Colbeck, Roger, Renner, Renato

Understand

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.

Built on

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Similar

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T. Holenstein and R. Renner, “On the randomness of independent experiments,” 2006. [Online]. Available: http://arxiv.org/abs/cs/0608007
2006
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Then

M. Hayashi, Quantum Information — An Introduction . Springer, 2006
2006
Later among the works it cites.
B. Schoenmakers, J. Tjoelker, P. Tuyls, and E. Verbitskiy, “Smooth Rényi entropy of ergodic quantum information sources,” in Proc. ISIT, 2007 , pp. 256–260
2007
Later among the works it cites.
K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: The quantum chernoff bound,” Phys. Rev. Lett. , vol. 98, no. 16, p. 160501, 2007
2007
Later among the works it cites.
R. König, R. Renner, and C. Schaffner, “The operational meaning of min- and max-entropy,” Jul. 2008. [Online]. Available: http://arxiv.org/abs/0807.1338
Original
2008
Closest in time.
M. Mosony and N. Datta, “Generalized relative entropies and the capacity of classical-quantum channels,” 2008. [Online]. Available: http://arxiv.org/abs/0810.3478
Original
2008
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N. Datta, “Min- and max- relative entropies and a new entanglement monotone,” Mar. 2008. [Online]. Available: http://arxiv.org/abs/0803.2770v1
Original
2008
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N. Datta and R. Renner, “Smooth Rényi entropies and the quantum information spectrum,” Jan. 2008. [Online]. Available: http://arxiv.org/abs/0801.0282
Original
2008
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M. Tomamichel, R. Colbeck, and R. Renner, “On the smoothing of conditional min- and max-entropies,” Unpublished Notes, 2009
2009
Closest in time.

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