Testing Born's Rule in Quantum Mechanics for Three Mutually Exclusive Events

We present a new experimental approach using a three-path interferometer and find a tighter empirical upper bound on possible violations of Born's Rule. A deviation from Born's rule would result in multi-order interference. Among the potential systematic errors that could lead to an apparent violation we specifically study the nonlinear response of our detectors and present ways to calibrate this error in order to obtain an even better bound.Comment: 10 pages, 5 figures, accepted for publication in Found. Phy