Multisetting Bell inequalities for N spin1 systems avoiding the KochenSpecker contradiction
Abstract
Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell inequalities is to assume the existence of a joint probability distribution for measurement results for all settings in the given experiment. However, for spin1 systems, one faces the problem that the eigenvalues of observables do not allow a consistent algebra if one allows all possible settings on each side (Bell's 1966 contradiction), or some specific sets (leading to a KochenSpecker 1967 contradiction). We show here that by choosing a special set of settings which never lead to inconsistent algebra of eigenvalues, one can still derive multisetting Bell inequalities, and that they are robustly violated. Violation factors increase with the number of subsystems. The inequalities involve only spin observables, we do not allow all possible qutrit observables, still the violations are strong.
 Publication:

Physical Review A
 Pub Date:
 September 2012
 DOI:
 10.1103/PhysRevA.86.032111
 arXiv:
 arXiv:1205.1399
 Bibcode:
 2012PhRvA..86c2111D
 Keywords:

 03.65.Ud;
 03.67.a;
 Entanglement and quantum nonlocality;
 Quantum information;
 Quantum Physics
 EPrint:
 6 pages, 4 figures, Published version, Phys. Rev. A 86, 032111