Quantum de Finetti theorem

The quantum de Finetti theorem represents every infinitely exchangeable quantum state as a mixture of independent identically distributed product states. Finite versions approximate a fixed-size marginal of an $N$-exchangeable state by such a mixture with error tending to zero as $N$ grows.

For a permutation-symmetric many-body problem with diverging coordination, finite-site reduced states approach mixtures of product states. Minimizing a local energy therefore reduces asymptotically to minimizing it over one-site density matrices, with separate one-site states allowed for distinct sublattices.