Fig. 4: Increasing levels for tight NPA upper bounds in the CHSH scenario.
From: Self-testing tilted strategies for maximal loophole-free nonlocality
A plot of the minimum level L ∈ {1, 1 + AB, 2, 3, 4, 5, 6, 7+} of the NPA hierarchy required to saturate the maximum quantum value \({c}_{{\mathcal{Q}}}(\alpha ,\beta )\) of the doubly-tilted CHSH inequality (15) such that \({c}_{{{\mathcal{Q}}}_{L}}(\alpha ,\beta )={c}_{{\mathcal{Q}}}(\alpha ,\beta )\) for α, β ∈ [0, 2]. Notably, while level 1 + AB suffices when either α = 0 (x-axes) or β = 0 (y-axes), the required minimum level of the NPA hierarchy rapidly increases as the tilting parameters tend toward the critical boundary α + β = 2.
