Quantum Entanglement and Chocolates

Two statistical ensembles of chocolates are constructed to mimic two quantum entangled states, the spin singlet state and the GHZ state. Despite great efforts to achieve the closest possible resemblance in terms of probability distribution and correlation, subtle differences remain. The differences reveal and illustrate a fundamental characteristic that distinguishes quantum entanglement from classical correlation. Analysis shows that the cause of this correlation discrepancy can be traced to the non-commutativity of quantum single-particle operators.