Describe the fundamental difference in the correlation properties between classically correlated systems and quantum entangled systems, especially regarding measurements on spatially separated parts.

Classically correlated systems exhibit correlations that arise from shared past events or pre-existing, locally defined properties. If you have two coins that are rigged to always land on the same side, they are classically correlated: knowing the outcome of one coin immediately tells you the outcome of the other. The correlation is based on prior knowledge and doesn't violate locality – the state of one coin doesn't instantly affect the other. Quantum entangled systems, in contrast, exhibit corr....