Many-particle interference to test Born's rule

Born's rule relates detection probabilities to the modulus square of the wave function. It is one of the central principles of quantum mechanics together with that of linear superposition. Single-particle interference is accordingly limited to pairs of quantum paths and higher-order interferences are prohibited. Deviations from Born's law have been quantified via the Sorkin parameter which is proportional to the third-order term. However, while the linearity of quantum theory has been experimentally tested to the level of 10^{−20} eV, the Sorkin parameter has only been measured to an accuracy of 2×10^{−3} in the quantum regime. We here investigate Born's law using many-particle interferences and demonstrate that all interference terms of order (2M+1) and greater vanish for M particles. We further introduce a family of many-particle Sorkin parameters and show that they are exponentially more sensitive to deviations from Born's rule than their single-particle counterpart.