  We present a new description of the known large deviation function of the
classical symmetric simple exclusion process by exploiting its connection with
the quantum symmetric simple exclusion processes and using tools from free
probability. This may seem paradoxal as free probability usually deals with non
commutative probability while the simple exclusion process belongs to the realm
of classical probability. On the way, we give a new formula for the free energy
-- alias the logarithm of the Laplace transform of the probability distribution
-- of correlated Bernoulli variables in terms of the set of their cumulants
with non-coinciding indices. This latter result is obtained either by
developing a combinatorial approach for cumulants of products of random
variables or by borrowing techniques from Feynman graphs.
