Non-Boolean Hidden Variables model reproduces Quantum Mechanics' predictions for Bell's experiment

Abstract

A hidden variables model complying with the simplest form of Local Realism is presented, which reproduces Quantum Mechanics' predictions for an even ideally perfect Bell's experiment. This is possible thanks to a vector hidden variable and the corresponding operation (projection), which do not hold to Boolean logic. The model is also able to sketch Hong-Ou-Mandel and entanglement swapping experiments. It completes, in the EPR-sense, the description of the physical reality of an entangled state of two qubits.Comment: 14 pages, 2 figure; supplementary information has 12 pages, 5 figure