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 measurement. We first provide the definition of the confidence of measurement as well as its useful properties for various types of multipartite measurement. We show that globally-maximum confidence that cannot be achieved by local operations and classical communication strongly depends on the existence of a certain type of entanglement witness. We also provide conditions for an upper bound on maximum of locally-achievable confidence. Finally, we establish a method in terms of entanglement witness to construct quantum state ensembles with nonlocal maximum confidence.
We investigate a witness for nonclassical multipartite states based on their disturbance under local measurements. The witness operator provides a sufficient condition for nonclassicality that coincides with a nonvanishing global quantum discord, but it does not demand an extremization procedure. Moreover, for the case of
Z2-symmetric systems, we rewrite the witness in terms of correlation functions so that classicality is found to necessarily require either vanishing magnetization in the invariant axis or isotropy of the two-point function in the transverse spin plane. We illustrate our results in quantum spin chains, where a characterization of factorized ground states (with spontaneously broken
Z2 symmetry) is achieved. As a by-product, the witness is also shown to indicate a second-order quantum phase transitions, which is illustrated for both the
XY and the Ashkin-Teller spin chains.
Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of the Hahn-Banach theorem to separate classical states from nonclassical ones. Nonclassicality linear witnesses are constructed, based on the observables available in a given physical situation. Some examples of nonclassical states are considered, with detection schemes available nowadays. Reviewing the concept of entanglement potential from a different perspective, it is shown that in some contexts an arbitrary single-system nonclassical state can be converted into a bipartite entangled state, provided a generalized controlled-displacement (e.g., beam-splitter, CNOT gate) is available. Also, this entanglement can be detected in a simple way using the nonclassicality witness of the original single-system state. Finally, we extend the discussion to multipartite states, proposing alternative ways to generate and classify multipartite entanglement.