Does there exist a super-quantum correlation in mixed-state formalism

[jk22]

Suppose a two point covariance : $C(a,b)=\langle A\otimes B\rangle$ with the eigenvalues of A and B in {-1,1}.

Does there exist a mixed state such that $CHSH=C(a,b)-C(a,b')+C(a',b)+C(a',b')>2\sqrt{2}$ ?

 

[A. Neumaier]

Any tiny perturbation of the density matrix of a pure state with this property should do...

 

[jk22]

So violation of Tsirelson's bound were possible ?

 

[A. Neumaier]

So violation of Tsirelson's bound were possible

Of course. If one uses in the standard experiments imperfect polarizers one gets preparations in mixed states; these effects are accounted for in efficiency analyses of entanglement experiments.