Born Rule(s)

Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)This paper is based on work published in [1]. It describes a triple slit experiment using single photons that has been used to provide a bound on one of the most fundamental axioms of quantum mechanics i.e. Born's rule for probabilities [2]. In spite of being one of the most successful theories which describes various natural phenomena, quantum mechanics has enough intricacies and ``weirdness'' associated with it which makes many physicists believe that it may not be the final theory and hints towards the possibility of more generalized versions. Quantum interference as shown by a double slit diffraction experiment only occurs from pairs of paths. Even in multi-slit versions, interference can only occur between pairs of possibilities and increasing the number of slits does not increase the complexity of the theory that still remains second-order. However, more generalized versions of quantum mechanics may allow for multi-path i.e. higher than second order interference. This experiment also provides a bound on the magnitude of such higher order interference. We have been able to bound 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