In the (2,2,2) Bell scenario, every fixed finite NPA level strictly over-approximates the quantum correlation set, because any bounded error would force the Motzkin polynomial plus a constant to be a sum of squares, which is impossible.
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No Finite NPA Level Characterizes the Complete Quantum Set in the Simplest Bell Scenario
In the (2,2,2) Bell scenario, every fixed finite NPA level strictly over-approximates the quantum correlation set, because any bounded error would force the Motzkin polynomial plus a constant to be a sum of squares, which is impossible.