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Baez, Fritz, and Leinster derived a method for characterizing Shannon entropyin classical systems. In this method, they considered a functor from a certaincategory to the monoid of non-negative real numbers with addition as a map frommeasure-preserving functions to non-negative real numbers, and derived Shannonentropy by imposing several simple conditions. We propose a method forcharacterizing von Neumann entropy by extending their results to quantumsystems.

A characterization of von Neumann entropy using functors