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
Green’s function
Two particle density matrix
Finite temperature two body Green’s function
HF approx.
One particle density matrix and One body Green’s function

where
,
then
and
• If
where
In
basis
Generalized
Werner State
where
Separability criterion=PPT= p 
&
1
3 always satisfied since
No entanglement in two-spin density matrix of non-interacting thermal
boson!
Classical correlation for BB radiation
Fidelity
Temperature dependency
where
Classical correlation
,
,
Classical correlation
f (r~ )
5I (~
r)
Aspect type experiment
a,a’
b,b’
Bell-CHSH inequality
| C (a, b)  C (a' , b)  C (a, b' )  C (a' , b' ) | 2
C (a, b)   AB( A, B | a, b)
A, B
A, B  1
Fermion Case
Conclusion



No two-spin entanglement in noninteracting thermal boson system
Useful for determining the character of
light sources
Need to study interacting case and
system with phase transition