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Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
By introducing a quantitative ``degree of commutativity'' in terms of the angle between spin observables we present two tight quantitative trade-off relations in the case of two qubits. First, for entangled states, between the degree of commutativity of local observables and the maximal amount of violation of the Bell inequality: …