2. Introduction
Is there entanglement of black body radiation such as cosmic background radiation or black hole radiation?
Entanglement of non-interacting Fermi gases
Creation of entanglement by interacting with thermal bath

3. Green’s function HF approx. where , Two particle density matrix
Finite temperature two body Green’s function
HF approx.
One particle density matrix and One body Green’s function
where ,

4. If
and
then
where In
basis
Generalized
Werner State
where
&
Separability criterion=PPT=
always satisfied since
No entanglement in two-spin density matrix of non-interacting thermal
boson!

5. Classical correlation for BB radiation
Fidelity
Temperature dependency
where , ,
Classical correlation

6. Classical correlation

7. Aspect type experiment
a,a’
b,b’
Bell-CHSH inequality

8. Fermion Case

9. Conclusion
No two-spin entanglement in non-interacting thermal boson system
Useful for determining the character of light sources
Need to study interacting case and system with phase transition