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

TL;DR

This study tests the Born rule in quantum mechanics by measuring three-path interference in NMR experiments, confirming the rule's predictions within experimental bounds.

Contribution

It provides an experimental test of the Born rule's prediction that three-path interference does not occur, using NMR techniques to measure interference ratios.

Findings

Three-path interference ratio bounded to ~10^{-3}

Results consistent with Born's rule

Supports the foundational assumption of quantum mechanics

Abstract

The Born rule is at the foundation of quantum mechanics and transforms our classical way of understanding 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 paths) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three path intereference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance (LSNMR). 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 $10^{-3} \pm 10^{-3}$, and hence it is consistent with Born's rule.