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Quantum many-body states that appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a correction term that is independent of its size. We recently showed that these states have an efficient dual description in terms of a set of marginal density matrices on bounded regions, obeying the same entropy scaling law locally. This leads to a characterization of a many-body quantum state in terms of its marginal density matrices, and moreover leads to a closed-form expression for the maximum entropy compatible with those marginals. I will explain the basic ideas behind these proofs, and discuss possible applications.

Based on arXiv:2010.07424 and arXiv:2109.11688.

This will be an in person talk.