Fig. 2: Self-testing of non-maximally incompatible measurements and non-maximally entangled state.
From: Self-testing tilted strategies for maximal loophole-free nonlocality
Plots of (i.) (solid blue line) the optimal cosine cA = cB = c*(α) (16), and (ii.) (dashed orange line) the Schmidt coefficient ξ* of the optimal non-maximally entangled quantum state \(\left\vert \psi \right\rangle ={\xi }^{* }\left\vert 00\right\rangle +\sqrt{1-{{\xi }^{* }}^{2}}\left\vert 11\right\rangle\) (represented in the Schmidt basis), against the tilting parameter α ∈ [0, 1), self-tested by the maximal quantum value \({C}_{\alpha ,\alpha }({\boldsymbol{p}})={c}_{{\mathcal{Q}}}(\alpha ,\alpha )\) of the symmetrically (α = β) tilted CHSH inequality (15). As α → 1 (\(\eta \to \frac{2}{3}\)), the optimal qubit measurements as well as the optimal two-qubit entangled state become almost compatible and product, respectively.
