Bell nonlocality and Kochen-Specker contextuality are two remarkable nonclassical features of quantum theory, related to strong correlations between outcomes of measurements performed on quantum systems. Both phenomena can be witnessed by the violation of certain inequalities, the simplest and most important of which are the Clauser-Horne-Shimony-Holt (CHSH) and the Klyachko-Can-Binicioğlu-Shumovski (KCBS), for Bell nonlocality and Kochen-Specker contextuality, respectively. It has been shown that, using the most common interpretation of Bell scenarios, quantum systems cannot violate both inequalities concomitantly, thus suggesting a monogamous relation between the two phenomena. In this Letter, we show that the joint consideration of the CHSH and KCBS inequalities naturally calls for the so-called generalized Bell scenarios, which, contrary to the previous results, allows for joint violation of them. In fact, this result is not a special feature of such inequalities: We provide very strong evidence that there is no monogamy between nonlocality and contextuality in any scenario where both phenomena can be observed. We also implement a photonic experiment to test the synchronous violation of both CHSH and KCBS inequalities. Our results agree with the theoretical predictions, thereby providing experimental proof of the coexistence of Bell nonlocality and contextuality in the simplest scenario, and lead to novel possibilities where both concepts could be jointly employed for quantum information processing protocols.
Peng Xue 1,*, Lei Xiao1, G. Ruffolo2, A. Mazzari 2, T. Temistocles 3,4, M. Terra Cunha5, and R. Rabelo 2,†1Beijing Computational Science Research Center, Beijing 100084, China2Instituto de Física “Gleb Wataghin,” Universidade Estadual de Campinas, 130830-859 Campinas, Brazil3Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 30123-970 Belo Horizonte, Brazil4Instituto Federal de Alagoas—Campus Penedo, 57200-000, Penedo, Alagoas, Brazil5Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, 130830-859 Campinas, Brazil