Multisetting Bell inequalities for N spin-1 systems avoiding the Kochen-Specker contradiction

摘要

Bell’s theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem.nOne of the methods to derive Bell inequalities is to assume the existence of a joint probability distribution fornmeasurement results for all settings in the given experiment. However, for spin-1 systems, one faces the problemnthat the eigenvalues of observables do not allow a consistent algebra if one allows all possible settings on eachnside (Bell’s 1966 contradiction), or some specific sets (leading to a Kochen-Specker 1967 contradiction). Wenshow here that by choosing a special set of settings which never lead to inconsistent algebra of eigenvalues, onencan still derive multisetting Bell inequalities, and that they are robustly violated. Violation factors increase withnthe number of subsystems. The inequalities involve only spin observables, we do not allow all possible qutritnobservables, still the violations are strong.