Analytic Qubit Separation between POVMs and Projective Measurements
Published in arXiv preprint, 2026
This work gives a fully analytic Bell-functional separation between general qubit POVMs and qubit projective measurements without enlarging the local dimension. A concrete rational three-outcome POVM achieves $2\sqrt{2}+1/100$, while a certified upper bound on all projective strategies establishes a gap greater than $1/1000$. A Lean proof certificate accompanies the separation theorem, and an exact level-3 noncommutative sum-of-squares certificate shows that the proposed qubit strategy reaches the unrestricted finite-dimensional tensor-product optimum.