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• W4297243522 abstract "Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set BQ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, BQ is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that BQ is strictly contained in an easy-to-characterize set associated with a graph, Θ(G). Therefore, whenever the optimum over BQ and the optimum over Θ(G) coincide, self-testing can be demonstrated by simply proving self-testability with Θ(G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araújo et al., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovász theta number for a family of graphs called the Möbius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1), this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.Received 13 December 2021Revised 6 August 2022Accepted 1 September 2022DOI:https://doi.org/10.1103/PRXQuantum.3.030344Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonlocalityQuantum correlations in quantum informationQuantum entanglementQuantum Information" @default.
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• W4297243522 date "2022-09-26" @default.
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• W4297243522 title "Graph-Theoretic Approach for Self-Testing in Bell Scenarios" @default.
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• W4297243522 doi "https://doi.org/10.1103/prxquantum.3.030344" @default.
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