  The set of states on ${\rm CCR}(\ch)$, the CCR algebra of a separable Hilbert
space $\ch$, is here looked at as a natural object to obtain a non-commutative
version of Freedman's theorem for unitarily invariant stochastic processes. In
this regard, we provide a complete description of the compact convex set of
states of ${\rm CCR}(\ch)$ that are invariant under the action of all
automorphisms induced in second quantization by unitaries of $\ch$. We prove
that this set is a Bauer simplex, whose extreme states are either the canonical
trace of the CCR algebra or Gaussian states with variance at least $1$.
