  We introduce a hierarchical classification of theories that describe systems
with fundamentally limited information content. This property is introduced in
an operational way and gives rise to the existence of mutually complementary
measurements, i.e. a complete knowledge of future outcome in one measurement is
at the expense of complete uncertainty in the others. This is characteristic
feature of the theories and they can be ordered according to the number of
mutually complementary measurements which is also shown to define their
computational abilities. In the theories multipartite states may contain
entanglement and tomography with local measurements is possible. The
classification includes both classical and quantum theory and also generalized
probabilistic theories with higher number of degrees of freedom, for which
operational meaning is given. We also discuss thought experiments
discriminating standard quantum theory from the generalizations.
