Contextuality of a two-qubit state in 4-cycle measurement scenarios

Abstract

We introduce a quantity of contextuality, i.e. the maximum contextuality of a two-qubit state in 4-cycle measurement scenarios, to study quantum contextuality of two-qubit states for the 4-cycle noncontextual inequalities. Subsequently, we prove several appealing features of this quantity of contextuality, including the faithfulness, the boundedness, the invariance under unitary operations and the convexity. Remarkably, for arbitrary two-qubit state, we reformulate this quantity of contextuality analytically by eigenvalues of the state. Therefore, in 4-cycle measurement scenarios, we establish an efficient way to distinguish two-qubit states that can reveal contextuality from ones that cannot.