Fig. 7: Self-testing of partially incompatible observables.
From: Self-testing tilted strategies for maximal loophole-free nonlocality
A plot of the optimal cosines of Alice \({c}_{A}^{* }(\alpha ,\beta )\) (16) with β ∈ {α, 0.1, 0.01, 0.001, 0} self-tested by the maximum quantum value \({C}_{\alpha ,\beta }({\boldsymbol{p}})={c}_{{\mathcal{Q}}}(\alpha ,\beta )\) of the doubly-tilted CHSH inequalities (15) against the tilting parameter α ∈ [0, 1]. Here, \({c}_{A}^{* }(\alpha ,\beta )=0\) implies maximally incompatible whereas \({c}_{A}^{* }(\alpha ,\beta )=1\) reflects compatible observables. Notice, that in contrast to the asymmetrically tilted case β = 0 wherein Alice’s optimal cosine \({c}_{A}^{* }(\alpha ,\beta =0)\) stays constant with respect to α18, for the general case, whenever β > 0, Alice’s optimal measurements change with \(\alpha =\frac{2}{{\eta }_{B}}(1-{\eta }_{B})\) and in-turn depend on Bob’s detection efficiency ηB, and tend towards compatible measurements as α → 2 − β.
