  A simple expression to compute the quantum discord between two orbitals in
fermion systems is derived using the parity superselection rule. As the
correlation between orbitals depends on the basis chosen, we discuss a special
orbital basis, the natural one. We show that quantum correlations between
natural orbital pairs disappear when the pairing tensor is zero, i.e. the
particle number symmetry is preserved. The Hartree-Fock orbitals within a
Slater determinant state, a Hartree-Fock-Bogoliubov quasiparticle orbitals in a
quasiparticle vacuum, or the ground state of a Hamiltonian with particle
symmetry and their corresponding natural orbitals are some relevant examples of
natural basis and their corresponding states. Since natural orbitals have that
special property, we seek for the quantum discord in non-natural orbital basis.
We analyze our findings in the context of the Lipkin-Meshkov-Glick and Agassi
models.
