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

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

The distinctive symmetry of Bell states

The Bell's basis is composed of four maximally entangled states of two qubits, named Bell states. They are usual tools in many theoretical studies and experiments. The aim of this paper is to find out the symmetries that determine a Bell state. For this purpose, starting from a general density matrix, physical constraints and symmetry conditions are added until the elements of the Bell's basis are univocally determined. It is found that the usual physical constraints and symmetry conditions do not suffice to determine a Bell state. The additional restriction needed is named here atomic symmetry. It is a sort of global symmetry of the system, not derived from the action = reaction law. It is also found that the imperfection in fulfilling the atomic symmetry is linearly proportional to the deviation of the Concurrence from its maximum value. The atomic symmetry allows a different insight on the nature of entanglement, and might be useful as a criterion to define the condition of maximal entanglement for states with more than two qubits.Comment: 8 pages, no figures, 1 appendi