Many-particle interference to test Born's rule

TL;DR

This paper extends the formalism of Born's rule testing to many-particle interference, revealing a richer structure and demonstrating that certain higher-order interference terms vanish, with increased sensitivity to deviations.

Contribution

It introduces a new framework for analyzing many-particle interference and shows that these interferences are more sensitive to potential deviations from Born's rule.

Findings

All interference terms of order (2M+1) and higher vanish for M particles.

Many-particle Sorkin parameters are exponentially more sensitive to deviations.

The formalism reveals a richer structure in many-particle interference patterns.

Abstract

Born's rule, one of the cornerstones of quantum mechanics, relates detection probabilities to the modulus square of the wave function. 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. We here extend this formalism to many-particle interferences and find that they exhibit a much richer structure. We demonstrate, in particular, 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.