Graph-Theoretic Approach for Self-Testing in Bell Scenarios

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