Three Slits Rule Out Multi-Order Interference

Full text: Sorkin investigated the possibility that quantum mechanics might be formulated as a generalized measure theory. Born's rule that quantum mechanical probabilities are absolute squares of complex amplitudes results in the interference of possible evolutions, just like in the interference of classical waves. Quantum mechanical interference violates the sum rule that probabilities of mutually exclusive events can be added. One can imagine a yet more general theory by assuming that it violates the next higher sum rule about the additivity of probabilities of three mutually exclusive possibilities. Standard quantum mechanics does obey this second sum rule and so does any classical wave theory. In other words, interference only occurs from all possible pairwise combinations of possibilities. A violation of that second sum rule would mean that there is higher order interference and that Born's rule would have to be modified. This would have dramatic implications, most likely resulting in a nonlinear theory. It has further been shown that a modification of Born's rule would allow computation that is more powerful than quantum computation, as well as perfect distinction of non-orthogonal quantum states. The latter would render quantum key distribution as we know it impossible. We experimentally tested the validity of the second sum rule by measuring the interference patterns produced by three slits and all the possible combinations of these slits being open or closed. We use either attenuated laser light or a heralded single photon source combined with single photon counting to confirm the particle character of the measured light. Within our experimental accuracy and Born's rule is vindicated and the second sum rule appears to be obeyed. (author)