Quantum violations in the Instrumental scenario and their relations to the Bell scenario

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.Comment: 12 pages, 3 figures. Comments welcome! v4: published version in Quantum journa

Comparison of two bounds of the quantum correlation set

Abstract — From a geometric viewpoint, quantum nonlocality between two parties is represented as the difference of two convex bodies, namely the sets of possible results of classical and quantum correlation experiments, the latter of which is called the quantum correlation set. Whereas little is known about the quantum correlation set, Tsirelson’s theorem (1980) can be seen as the exact characterization of possible pairwise quantum correlations, where mean values of individual observables are discarded. In this paper, we compare two previously shown bounds of the quantum correlation set in the case where two parties have m and n choices of dichotomic observables, respectively. One bound comes from the direct application of Tsirelson’s theorem and the no-signalling condition. The other bound, recently introduced by Avis, Imai and Ito, refines the application of Tsirelson’s theorem in the previous bound. We show that for any m, n ≥ 2, this ne