Exponential de Finetti Theorems for Fermionic Gaussian States
The paper proves an exponential variant of de Finetti theorems for free-fermionic Gaussian states. It shows that subsystems of permutation-invariant, free-fermionic Gaussian states can be approximated by convex combinations of almost-i.i.d. states with a super-exponential error decay in the number of unconstrained parts, significantly improving upon standard de Finetti results.