A Third Information-Theoretic Approach to Finite de Finetti Theorems

04/11/2023

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by   Mario Berta, et al.

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A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first k random variables in an exchangeable vector of n≥ k random variables is close to a mixture of product distributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided. This bound is tighter than those obtained via earlier information-theoretic proofs, and its utility extends to random variables taking values in general spaces. The core argument employed has its origins in the quantum information-theoretic literature.