Invariance under energy-preserving unitaries forces large-N reduced states to be close to thermal mixtures, with vanishing error bounds.
(C24) and (C25), we have ProjK =MatK=I−K −1C T (CK −1C T )−1C.(C27) Thus,K −1C T (CK −1C T )−1C=I−Proj K is a projector and 111T K −1C T (CK −1C T )−1C111≥0
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Symmetry-driven thermalization via finite de Finetti theorems
Invariance under energy-preserving unitaries forces large-N reduced states to be close to thermal mixtures, with vanishing error bounds.