Is there three-path interference beyond what the Born rule allows?
In plain words
The Born rule implies that interference always comes from pairs of paths, so a three-slit pattern is fixed by the two-slit and one-slit patterns. A leftover three-path term would show the Born rule is wrong.
Precise statement
Sorkin's third-order term $I_3 = P_{ABC} - P_{AB} - P_{AC} - P_{BC} + P_A + P_B + P_C - P_0$ ($P_S$ = detection probability with slit set $S$ open) vanishes identically if $p = \mid \psi \mid^2$. Measure $\kappa = I_3 / \delta$, with delta a normalization such as the sum of magnitudes of the two-path interference terms, for photons, massive particles or many-particle states, and either detect $\kappa != 0$ or bound it below the systematic floor set by nonclassical looped paths.
What would settle it
A multi-path interferometer measurement with systematics, including looped-path corrections, controlled below the target $\kappa$.
Status in the literature
Unverified note
Photonic, NMR and single-spin tests since 2010 found $\kappa$ consistent with zero; 2024-2026 proposals and analyses extend the test to Bose-Einstein condensates, attosecond photoionization and collider scattering.