A single device-independent protocol certifies every d-dimensional d-partite supersinglet state (d>=3) by exhibiting a perfect quantum strategy: a pseudo-telepathy game that entangled parties win with probability one while no classical local-hidden-variable strategy can. The construction exploits the supersinglet's invariance under collective SU(d) rotations together with complete Kochen-Specker sets of measurements in C^d, yielding self-testing in which the shared state and the local measurements are pinned uniquely (up to a local isometry) from the observed correlations alone.
Supersinglets are total-spin-zero states of d particles of d levels (d >= 3), generalizing the two-qubit singlet; they are invariant under U^{tensor d} and appear in metrology, decoherence-free error…