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A new finite form of de Finetti's representation theorem is established usingelementary information-theoretic tools. The distribution of the first $k$random variables in an exchangeable vector of $n\geq k$ random variables isclose to a mixture of product distributions. Closeness is measured in terms ofthe relative entropy and an explicit bound is provided. This bound is tighterthan those obtained via earlier information-theoretic proofs, and its utilityextends to random variables taking values in general spaces. The core argumentemployed has its origins in the quantum information-theoretic literature.

A Third Information-Theoretic Approach to Finite de Finetti Theorems