Ensemble-averaged entanglement of two-particle states in Fock space

Recent results, extending the Schmidt decomposition theorem to wave functions of pairs of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band, and to a pair of bosons in a quadratic model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasized