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Question: Might there be a natural geometric interpretation of the exponential of entropy in Classical and Quantum Information theory? This question occurred to me recently via a geometric inequality ...

Let $\Omega$ be a countable set and $\mu,\nu\colon\Omega\to[0,1]$ be distributions on $\Omega$, that is we have $\sum_{x\in\Omega}\mu(x)=1$ and likewise for $\nu$. The Kullback-Leibler divergence of $\...