Quantum separability of thermal spin one boson systems

Using the temperature Green's function approach we investigate entanglement between two non-interacting spin 1 bosons in thermal equilibrium. We show that, contrary to the fermion case, the entanglement is absent in the spin density matrix. Separability is demonstrated using the Peres-Horodecki criterion for massless particles such as photons in black body radiation. For massive particles, we show that the density matrix can be decomposed with separable states