  We demonstrate that quantum incompatibility can always be detected by means
of a state discrimination task with partial intermediate information. This is
done by showing that only incompatible measurements allow for an efficient use
of premeasurement information in order to improve the probability of guessing
the correct state. Thus, the gap between the guessing probabilities with pre-
and postmeasurement information is a witness of the incompatibility of a given
collection of measurements. We prove that all linear incompatibility witnesses
can be implemented as some state discrimination protocol according to this
scheme. As an application, we characterize the joint measurability region of
two noisy mutually unbiased bases.
