Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule

Abstract

The Born rule is at the foundation of quantum mechanics and transforms the classical understanding of probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the Born rule is that three-way (or three-path) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three-path interference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance. As a measure of the consistency, we evaluate the ratio of three-way interference to two-way interference. Our experiment bounded the ratio to the order of 10 ^−3 ± 10 ^−3 , and hence it is consistent with Born's rule.