  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.
