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arXiv:2011.13790 · Physical Review Letters

Converting Contextuality into Nonlocality

Adán Cabello

Published Aug 11, 2021• 41 citations
arXivHTMLPDF

Abstract

We introduce a general method which converts, in a unified way, any form of quantum contextuality, including any form of state-dependent contextuality, into a quantum violation of a bipartite Bell inequality. As an example, we apply the method to a quantum violation of the Klyachko-Can-Binicioğlu-Shumovsky inequality.
DOI
10.1103/physrevlett.127.070401

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Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.
Quantum mechanics exhibits a very peculiar form of contextuality. Identifying and connecting the simplest scenarios in which more general theories can or cannot be more contextual than quantum mechanics is a fundamental step in the quest for the principle that singles out quantum contextuality. The former scenario corresponds to the Klyachko-Can-Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu-Shumovsky (KCBS) inequality. Here we show that there is a simple tight inequality, twin to the KCBS, for which quantum contextuality cannot be outperformed. In a sense, this twin inequality is the simplest tool for recognizing fully contextual quantum correlations.
Bell inequalities play a central role in the study of quantum nonlocality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality which can be used to systematically derive testable inequalities for a very wide variety of situations. There is a single clear conceptual principle, based on purely logical consistency conditions, which underlies our notion of logical Bell inequalities. We show that in a precise sense, all Bell inequalities can be taken to be of this form. Our approach is very general. It applies directly to any family of sets of commuting observables. Thus it covers not only the nnn-partite scenarios to which Bell inequalities are standardly applied, but also Kochen-Specker configurations, and many other examples. There is much current work on experimental tests for contextuality. Our approach directly yields, in a systematic fashion, testable inequalities for a very general notion of contextuality. There has been much work on obtaining proofs of Bell's theorem ``without inequalities'' or ``without probabilities.'' These proofs are seen as being in a sense more definitive and logically robust than the inequality-based proofs. On the hand, they lack the fault-tolerant aspect of inequalities. Our approach reconciles these aspects, and in fact shows how the logical robustness can be converted into systematic, general derivations of inequalities with provable violations. Moreover, the kind of strong non-locality or contextuality exhibited by the GHZ argument or by Kochen-Specker configurations can be shown to lead to maximal violations of the corresponding logical Bell inequalities. Thus the qualitative and the quantitative aspects are combined harmoniously.
This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to determine the quantum limit of Bell-type linear inequalities. In contrast to semidefinite programming approaches, our method allows for the consideration of inequalities with abstract weights, by means of leveraging the Hermiticity of quantum states. Recognizing that classical correlations correspond to measurements made on separable states, we also introduce a practical method for obtaining sufficient separability criteria. We specifically vet the candidacy of driven and undriven superradiance as schema for entanglement generation. We conclude by reviewing current approaches to quantum contextuality, emphasizing the operational distinction between nonlocal and contextual quantum statistics. We utilize our abstractly-weighted linear quantum bounds to explicitly demonstrate a set of conditional probability distributions which are simultaneously compatible with quantum contextuality while being incompatible with quantum nonlocality. It is noted that this novel statistical regime implies an experimentally-testable target for the Consistent Histories theory of quantum gravity.
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.