  A state discrimination problem in an operational probabilistic theory (OPT)
is investigated in diagrammatic terms. It is well-known that, in the case of
quantum theory, if a state set has a certain symmetry, then there exists a
minimum-error measurement having the same type of symmetry. However, to our
knowledge, it is not yet clear whether this property also holds in a more
general OPT. We show that it also holds in OPTs, i.e., for a symmetric state
set, there exists a minimum-error measurement that has the same type of
symmetry. It is also shown that this result can be utilized to optimize over a
restricted class of measurements, such as sequential or separable measurements.
