In quantum field theory, causality is imposed by demanding that field operators at spacetime points separated by spacelike intervals commute. However, time-ordered field correlation functions between such points can be finite, and is commonly understood to arise due to entanglement. (I read this in a comment by Gerard 't Hooft on <https://www.quantamagazine.org/20160517-pilot-wave-theory-gains-experimental-support/>)

However, it is possible to imagine situations with classical fields producing finite correlations at spacelike points. Imagine a spherical wave from a classical electromagnetic monochromatic point source. The electric fields at spacelike separated points on a large spherical wavefront can be perfectly correlated. 

The question then is, is there a quantitative relation between the strength of correlations at spacelike intervals possible in quantum field theory vs classical field theory? I believe this would be tantamount to a reformulation of Bell's theorem in the language of quantum field theory.