A Third Information-Theoretic Approach to Finite de Finetti Theorems

Mario Berta; Lampros Gavalakis; Ioannis Kontoyiannis

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arXiv · 2304.05360

A Third Information-Theoretic Approach to Finite de Finetti Theorems

Mario Berta·Lampros Gavalakis·Ioannis Kontoyiannis

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Abstract

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 $n\geq k$ 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.

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BibTeX RIS

Mario Berta, Lampros Gavalakis, Ioannis Kontoyiannis. 2023-04-11. A Third Information-Theoretic Approach to Finite de Finetti Theorems. https://arxiv.org/abs/2304.05360

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