  We provide a prescription to construct R\'{e}nyi and von Neumann entropy of a
system of interacting fermions from a knowledge of its correlation functions.
We show that R\'{e}nyi entanglement entropy of interacting fermions in
arbitrary dimensions can be represented by a Schwinger Keldysh free energy on
replicated manifolds with a current between the replicas. The current is local
in real space and is present only in the subsystem which is not integrated out.
This allows us to construct a diagrammatic representation of entanglement
entropy in terms of connected correlators in the standard field theory with no
replicas. This construction is agnostic to how the correlators are calculated,
and one can use calculated, simulated or measured values of the correlators in
this formula. Using this diagrammatic representation, one can decompose
entanglement into contributions which depend on the one-particle correlator,
two particle correlator and so on. We provide analytic formula for the
one-particle contribution and a diagrammatic construction for higher order
contributions. We show how this construction can be extended for von-Neumann
entropy through analytic continuation. For a practical implementation of a
quantum state, where one usually has information only about few-particle
correlators, this provides an approximate way of calculating entanglement
commensurate with the limited knowledge about the underlying quantum state.
