Experimental test of quantum contextuality

ContextualityNon-contextual theoriesAssume that A ∼ B and A ∼ C. A theory is non-contextual, if it assigns toA a value v(A) independently whether B or C is measured jointly with A.This definition needs at least 3 measurements.B and C don’t have to be compatible.Is this a reasonable assumption about theories ?KS Theorem: Such models are in conflict with quantum theoryUsual proof: If |ψ i 〉 form an orthonormal basis, then P i = |ψ i 〉〈ψ i | arecompatible. Non-contextual models have to assign to each P i a value {0, 1}independent of the complete basis. On can write down sets of bases, suchthat this cannot be done.A. Cabello, Int. J. Quantum Inf. 4, 55 (2006)