Testing Born's Rule in Quantum Mechanics with a Triple Slit Experiment

TL;DR

This paper reports an experiment testing the validity of a higher-order sum rule in quantum mechanics using a triple slit setup with single photons, aiming to explore potential deviations from standard quantum interference.

Contribution

It presents an experimental test of a higher-order sum rule in quantum mechanics, probing possible violations of Born's rule with a triple slit interference experiment.

Findings

No violation of the higher-order sum rule observed

Confirms quantum interference patterns with single photons

Supports the validity of Born's rule in the tested regime

Abstract

In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the resulting interference violates the (Kolmogorov) sum rule expressing the additivity of probabilities of mutually exclusive events. However, there is a higher order sum rule that quantum mechanics does obey, involving the probabilities of three mutually exclusive possibilities. We could imagine a yet more general theory by assuming that it violates the next higher sum rule. In this paper, we report results from an ongoing experiment that sets out to test the validity of this second sum rule by measuring the interference patterns produced by three slits and all the possible combinations of those slits being open or closed. We use attenuated laser light combined with single photon counting to confirm the particle character of the measured light.