  We reconstruct the transformations of quantum theory using a physically
motivated postulate. This postulate states that transformations should be
locally applicable, and recovers the linear unitary maps from pure quantum
theory, as well as the completely positive, trace-preserving maps from mixed
quantum theory. Notably, in the pure case, linearity with respect to the
superposition rule on Hilbert spaces is derived rather than assumed (and
without any continuity assumptions).
