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Reconstructing quantum theory

We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map between pure states and maximal effects such that we get unit probability. This maximal effect does not give probability equal to one for any other pure state. Information Locality: A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components. Tomographic Locality: The state of a composite system can be determined from the statistics collected by making measurements on the components. Permutability: There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. Sturdiness: Filters are non-flattening. To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.