Quantum correlations on the no-signaling boundary: self-testing and more

• URL: http://arxiv.org/abs/2207.13850v3
• Date: Wed, 5 Jul 2023 02:47:27 GMT
• Title: Quantum correlations on the no-signaling boundary: self-testing and more
• Authors: Kai-Siang Chen, Gelo Noel M. Tabia, Chellasamy Jebarathinam, Shiladitya Mal, Jun-Yi Wu, Yeong-Cherng Liang
• Abstract summary: We prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations. All correlations of $mathcalM$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements.
• Score: 0.39146761527401425
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing $k$ zero probabilities, we provide a $(5-k)$-parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set $\mathcal{M}$ of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of $\mathcal{M}$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.

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