Symmetric states on the CAR algebra

De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. Here we mainly report two extension of De Finetti Theorem in the case of the CAR algebra. Namely we firstly realize that the compact convex set of such states is a Choquet simplex, whose extremals are precisely the product states in the sense of Araki–Moriya. Then we present a so–called extended version of this result, showing that these states are conditionally independent w.r.t. the tail algebra.