Classical max-entropy, also called Hartley entropy, is the order-zero Rényi entropy of a discrete random variable,
Here and below,
is the base of the logarithm. 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.
,
is the base of the logarithm. Thus it depends only
on the support of the distribution and is the largest
of the Rényi entropies.
,
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).
