  The analysis of the entanglement entropy of a subsystem of a one-dimensional
quantum system is a powerful tool for unravelling its critical nature. For
instance, the scaling behaviour of the entanglement entropy determines the
central charge of the associated Virasoro algebra. For a free fermion system,
the entanglement entropy depends essentially on two sets, namely the set $A$ of
sites of the subsystem considered and the set $K$ of excited momentum modes. In
this work we make use of a general duality principle establishing the
invariance of the entanglement entropy under exchange of the sets $A$ and $K$
to tackle complex problems by studying their dual counterparts. The duality
principle is also a key ingredient in the formulation of a novel conjecture for
the asymptotic behavior of the entanglement entropy of a free fermion system in
the general case in which both sets $A$ and $K$ consist of an arbitrary number
of blocks. We have verified that this conjecture reproduces the numerical
results with excellent precision for all the configurations analyzed. We have
also applied the conjecture to deduce several asymptotic formulas for the
mutual and $r$-partite information generalizing the known ones for the single
block case.
