Classical max-entropy, also called Hartley entropy, is the order-zero Rényi entropy of a discrete random variable,
Thus it depends only on the support of the distribution
and is the largest of the Rényi entropies.
In one-shot quantum information, the same name is used for a different quantity. For a density matrix ,
the unconditioned quantum max-entropy is
which is the order-
quantum Rényi entropy rather than the order-zero
entropy. Conditional and smoothed versions are used in one-shot information theory
(König et al. 2009).
König, R.; Renner, R.; and Schaffner, C. "The Operational Meaning of Min- and Max-Entropy." IEEE Trans. Inform. Th.55,
4337-4347, 2009. https://doi.org/10.1109/TIT.2009.2025545.Rényi,
A. "On Measures of Entropy and Information." Proc. Fourth Berkeley Symp.
Math. Stat. and Probability, Vol. 1. Berkeley, CA: University of California
Press, pp. 547-561, 1961.
,
,
the unconditioned quantum max-entropy is
quantum Rényi entropy rather than the order-zero
entropy. Conditional and smoothed versions are used in one-shot information theory
(König et al. 2009).
