Bell-like inequalities from symmetrized products of noncommuting observables on qubits
Omar Gamel, Graham R. Fleming
It is well known that noncommuting observables cannot be simultaneously measured in quantum theory. However, under hidden variable models, such observables must simultaneously hold premeasurement values. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fr\'echet bounds, finding that the joint probabilities may be negative. We then use the symmetrization heuristic to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct generalized Bell inequalities with a quantum to classical violation of \frac{3}{2}. The result demonstrates the importance of noncommutativity in the nonclassicality of quantum mechanics. However, the additional symmetrization assumption makes its conclusions weaker than traditional Bell inequalities.
•Sep 28, 2015•0 citations