For questions about the observable phenomenon of correlations among distant observers being incompatible with classical explanations in the form of local hidden variable models. A common way to certify that a state allows observing this form of nonlocal correlations is the class of inequalities collectively referred to as Bell's inequalities. Other forms of nonlocality are possible, the phenomenon of "steering" being an example.
The phenomenon by which measurements made at a microscopic level can contradict a collection of notions known as "local realism" that are regarded as intuitively true in classical mechanics. Some observations about the correlations among multiple parties, while correctly predicted by quantum mechanics, can be proved to be impossible to achieve via local hidden variable theories.