# 1.2.5. Ruling Out Multi-Order Interference in Quantum Mechanics[4]

This article ruled out third- and higher-order interference and providing a bound on the accuracy of Born's rule.

The probability density to find a particle at position and at time is given by A double-slit diffraction experiment is a direct consequence of this rule; the probability to detect a particle at r after passing through an aperture with two slits, A and B, is given by The corresponding (second-order) interference term can be defined as We define the third- order interference term for a three-path configuration (mutually exclusive) as the deviation of from the sum of the individual probabilities and the second-order interference terms:

The nonzero interference term is expected in all wave theories, including quantum mechanics. The next higher-order (i.e., three-path) interference term will be zero in all wave theories, with a square-law relation between the field energy (or probability density) and field amplitude, which is the case in quantum mechanics with Born's rule. Moreover, if there is no interference at a certain level in the hierarchy, the higher-order terms must vanish as well.

We expect the three-path interference term to be zero, with the advantage of being independent of many experimental parameters, thus enabling a more precise null test for Born's rule.

To measure in various optical power regimes, we used different types of photon sources.

With a null experiment, a very careful analysis of random and systematic errors must be undertaken, as our bound on the amount of three-path interference will be directly related to the level of experimental uncertainty.

We are able to bound the magnitude of the third-order interference term to less than of the regular expected second-order interference, at several detector positions. Thus, our experiment is able to rule out the existence of third-order in- terference terms (and, in effect, any higher-order interference terms) up to this bound.