Abstract
R. D. Sorkin1 investigated the possibility that quantum mechanics might be formulated as a generalized measure theory. Born's rule stipulates that quantum mechanical probabilities are absolute squares of complex amplitudes. This results in the well-known phenomenon of interference and constitutes a violation of a sum rule for the additivity of probabilities of mutually exclusive events. 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. It has been shown that a violation of the second sum rule might allow computation that is more powerful than quantum computation.
© 2011 IEEE
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