  The formalism of general probabilistic theories provides a universal paradigm
that is suitable for describing various physical systems including classical
and quantum ones as particular cases. Contrary to the usual no-restriction
hypothesis, the set of accessible meters within a given theory can be limited
for different reasons, and this raises a question of what restrictions on
meters are operationally relevant. We argue that all operational restrictions
must be closed under simulation, where the simulation scheme involves mixing
and classical post-processing of meters. We distinguish three classes of such
operational restrictions: restrictions on meters originating from restrictions
on effects; restrictions on meters that do not restrict the set of effects in
any way; and all other restrictions. We fully characterize the first class of
restrictions and discuss its connection to convex effect subalgebras. We show
that the restrictions belonging to the second class can impose severe physical
limitations despite the fact that all effects are accessible, which takes
place, e.g., in the unambiguous discrimination of pure quantum states via
effectively dichotomic meters. We further demonstrate that there are physically
meaningful restrictions that fall into the third class. The presented study of
operational restrictions provides a better understanding on how accessible
measurements modify general probabilistic theories and quantum theory in
particular.
