  The uncertainty principle may be considered as giving rise to the notion of
incompatibility of observables. A pack of quantum measurements that cannot be
measured simultaneously is said to form a set of incompatible measurements.
Every set of incompatible measurements has an advantage over the compatible
ones in a quantum state discrimination task where one prepares a state from an
ensemble and sends it to another party, and the latter tries to detect the
state using available measurements. Comparison between global and local quantum
state discriminations is known to lead to a phenomenon of "nonlocality". In
this work, we seal a connection between the domains of local quantum state
discrimination and incompatible quantum measurements. We consider the local
quantum state discrimination task where a sender prepares a bipartite state and
sends the subsystems to two receivers. The receivers try to detect the sent
state using locally incompatible measurements. We analyze the ratio of the
probability of successfully guessing the state using incompatible measurements
and the maximum probability of successfully guessing the state using compatible
measurements. We find that this ratio is upper bounded by a simple function of
robustnesses of incompatibilities of the local measurements. Interestingly,
corresponding to every pair of sets of incompatible measurements, there exists
at least one local state discrimination task where this bound can be achieved.
We argue that the optimal local quantum state discrimination task does not
present any "nonlocality", where the term is used in the sense of a difference
between the ratios, of probabilities of successful detection via incompatible
and compatible measurements, in global and local state discriminations. The
results can be generalized to the regime of multipartite local quantum state
distinguishing tasks.
