Simultaneous All-versus-Nothing Refutation of Local Realism and Noncontextuality by a Single System

The quantum realms of nonlocality and contextuality are delineated by Bell's theorem and the Kochen-Specker theorem, respectively, embodying phenomena that surpass the explanatory capacities of classical theories. These realms hold transformative potential for the fields of information and computing technology. In this study, we unveil a ``all-versus-nothing" proof that concurrently illustrates the veracity of these two seminal theorems, fostering a more nuanced comprehension of the intricate relationship intertwining quantum nonlocality and contextuality. Leveraging the capabilities of three singlet pairs and a Greenberger-Horne-Zeilinger state analyzer, our proof not only substantiates the conflict between quantum mechanics and hidden-variable theories from another perspective, but can also be readily verifiable utilizing the existing linear optics technology.