  We consider multipartite quantum state discrimination and provide a specific
relation between the properties of entanglement witness and quantum nonlocality
inherent in the confidence of measurements. We first provide the definition of
the confidence of measurements as well as its useful properties for various
types of multipartite measurements. We show that globally maximum confidence
that cannot be achieved by local operations and classical communication
strongly depends on the existence of entanglement witness. We also provide
conditions for an upper bound on maximum of locally-achievable confidences.
Finally, we establish a method in terms of entanglement witness to construct
quantum state ensemble with nonlocal maximum confidences.
