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Min-Entropy

The min-entropy of a discrete random variable X is the order-infinity Rényi entropy

H_infty(X)=-log_bmax_(x)p(x).

Thus b^(-H_infty(X)) is the largest probability of any outcome, and H_infty(X)<=H_b(X), where H_b(X) is the Shannon entropy. Conditional and smoothed min-entropies are used in randomness extraction and one-shot information theory (König et al. 2009).

See also

Max-Entropy, Rényi Entropy, Shannon Entropy

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References

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.

Cite this as:

Weisstein, Eric W. "Min-Entropy." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Min-Entropy.html

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