  Some quantum measurements can not be performed simultaneously, i.e. they are
incompatible. Here we show that every set of incompatible measurements provides
an advantage over compatible ones in a suitably chosen quantum state
discrimination task. This is proven by showing that the Robustness of
Incompatibility, a quantifier of how much noise a set of measurements tolerates
before becoming compatible, has an operational interpretation as the advantage
in an optimally chosen discrimination task. We also show that if we take a
resource-theory perspective of measurement incompatibility, then the guessing
probability in discrimination tasks of this type forms a complete set of
monotones that completely characterize the partial order in the resource
theory. Finally, we make use of previously known relations between measurement
incompatibility and Einstein-Podolsky-Rosen steering to also relate the later
with quantum state discrimination.
