Entanglement with classical fields

A simple classical-field optical heterodyne method which employs postselection to reproduce the polarization correlations of four-particle entangled state was experimentally analyzed. A heuristic argument relating this method to the measurement of multiple quantum fields by correlated homodyne detection was given. The polarization correlations of the 32 elements in the truth table from the quantum mechanical Greenberger-Horne-Zeilinger experiments on the violation of local realism were reproduced. A form of classical entanglement swapping in a four-particle basis was also demonstrated.