Standard quantum information theory is a GPT where system types are described by a natural number D which corresponds to the complex Hilbert space dimension. States of the systems of Hilbert space dimension D are described by the normalized positive semidefinite matrices, i.e. by the density matrices. Measurements are identified with Positive Operator valued Measures (POVMs), and the physical operations are completely positive maps. Systems compose via the tensor product of the underlying complex Hilbert spaces.