  Quantum mechanics and gravitation are two pillars of modern physics. Despite
their success in describing the physical world around us, they seem to be
incompatible theories. There are suggestions that one of these theories must be
generalized to achieve unification. For example, Born's rule, one of the axioms
of quantum mechanics could be violated. Born's rule predicts that quantum
interference, as shown by a double slit diffraction experiment, occurs from
pairs of paths. A generalized version of quantum mechanics might allow
multi-path, i.e. higher order interferences thus leading to a deviation from
the theory. We performed a three slit experiment with photons and bounded the
magnitude of three path interference to less than 10-2 of the expected two-path
interference, thus ruling out third and higher order interference and providing
a bound on the accuracy of Born's rule. Our experiment is consistent with the
postulate both in semi-classical and quantum regimes.
