Subsystems of permutation-invariant fermionic Gaussian states are exponentially well approximated by mixtures of almost-i.i.d. states, and all Gaussian-invariant states admit Gaussian-symmetric purifications.
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Exponential de Finetti Theorems for Fermionic Gaussian States
Subsystems of permutation-invariant fermionic Gaussian states are exponentially well approximated by mixtures of almost-i.i.d. states, and all Gaussian-invariant states admit Gaussian-symmetric purifications.