  Slater determinants are product states of filled quantum fermionic orbitals.
When they are expressed in a configuration space basis chosen a priori, their
entanglement is bound and controlled. This suggests that an exact
representation of Slater determinants as finitely-correlated states is
possible. In this paper we analyze this issue and provide an exact Matrix
Product representation for Slater determinant states. We also argue possible
meaningful extensions that embed more complex configuration interaction states
into the description.
