Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States
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We define a property called nondegeneracy for Bell inequalities, which describes the situation that in a Bell setting, if a Bell inequality and involved local measurements are chosen and fixed, any quantum state with a given dimension and its orthogonal quantum state cannot violate the inequality remarkably at the same time. We prove that for an arbitrary quantum dimension, based on the measurement statistics only, we can give an analytic lower bound for the entanglement of formation of the unknown bipartite quantum state by choosing a proper nondegenerate Bell inequality, making the whole process semi-device-independent. We provide specific examples to demonstrate the existence of nondegeneracy and applications of our approach.
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