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We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a welldefined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be welldefined. The four principles are: causality, purification, strong symmetry, and informationally consistent composition. Sorkin has (...) 