Not yet reviewed by Pith; the record is open.

The Bell inequality, and its substantial experimental violation, offers a seminal paradigm for showing that the world is not in fact locally realistic. Here, going beyond the scope of Bell's inequality on physical states, we show that quantum teleportation can be used to quantitatively characterize quantum correlations of physical processes. The validity of the proposed formalism is demonstrated by considering the problem of teleportation through a linear three-node quantum network. A hierarchy is derived between the Bell nonlocality, nonbilocality, steering and nonlocality-steering hybrid correlations based on a process fidelity constraint. The proposed framework can be directly extended to reveal the nonlocality structure of teleportation through any linear many-node quantum network. The formalism provides a faithful identification of quantum teleportation and demonstrates the use of quantum-information processing as a means of quantitatively discriminating quantum correlations.