# Does the violation of Bell inequality by a classical field imply "classical entanglement"?

This article has been brought to my attention recently (free access) : Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields

In the abstract, they claim that "The growing recognition that entanglement is not exclusively a quantum property [...] prompts the examination of its role in marking the quantum-classical boundary." To this purpose, they used a classical (statistically speaking) ergodic stochastic optical field and proved theoretically and experimentally that the CHSH inequality could be violated, if instead of using quantum states, one uses classical internal degrees of freedom of the field.

More precisely, they consider the case of completely unpolarized light for which it is impossible to write the electrical field as a product $E(t)\:\vec{u}$ for all $t$. Considering the temporal amplitude $E(t)$ and the polarization vector $\vec{u}$ as two internal degrees of freedom, they use linear algebra to show that the situation is equivalent to two entangled quantum states and that it then should violate Bell inequality.

I have no problem admitting that even for statistically classical fields, one can find strong correlations between two degrees of freedom, thus violating the CHSH inequality. But all that means to me is that, these degrees of freedom are not locally independent, ie that one cannot associate local hidden variables to each one of them that would explain the behaviour of the field. That doesn't mean at all that they are actually entangled, because for me entanglement is purely a quantum property.

My question is then the following : are strong classical correlations violating Bell inequality really implying any form of "classical entanglement" or is this just a fancy name ? A precise characterization of entanglement would also be appreciated to see if it is (as I thought until now) intrinsically a quantum property.

Thanks for the help.