A Separation between Full-Rank PVM and Assumption-free Self-Testing
Published in arXiv preprint, 2026
This work constructs a nonlocal game that self-tests a maximally entangled qubit strategy among pure full-Schmidt-rank projective strategies, yet also admits an inequivalent optimum using a nonprojective measurement. The result resolves a conjecture about imposing full rank and projectivity simultaneously. The optimal correlations of an auxiliary game are classified through tracial states, and a six-dimensional family shows that the resulting full-rank projective-measurement self-test is not robust.