Proposal for revealing quantum nonlocality via local contextuality

Two distant systems can exhibit quantum nonlocality even though the correlations between them admit a local model. This nonlocality can be revealed by testing extra correlations between successive measurements on one of the systems which do not admit a noncontextual model whatever the reduced state of this system is. This shows that quantum contextuality plays a fundamental role in quantum nonlocality, and allows an experimental test of the Kochen-Specker with locality theorem.