Abstract
Bell’s theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models. The violation of a Bell inequality, however, does not exclude classical models where some level of measurement dependence is allowed, that is, the choice made by observers can be correlated with the source generating the systems to be measured. Here, we show that the level of measurement dependence can be quantitatively upper bounded if we arrange the Bell test within a network. Furthermore, we also prove that these results can be adapted in order to derive nonlinear Bell inequalities for a large class of causal networks and to identify quantumly realizable correlations that violate them.3 MoreReceived 28 May 2021Accepted 23 September 2021DOI:https://doi.org/10.1103/PRXQuantum.2.040323Published 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 entanglementQuantum networksQuantum Information
Highlights
Bell’s theorem [1] can arguably be seen as the most radical departure from classical physics
As first pointed out by Brans [6], local-hidden-variable models are still capable of reproducing the quantum predictions if we allow for measurement dependence, a mechanism where our measurement devices are correlated with the system to be measured
By considering a slight modification of a Bell experiment, one had the means of determining an upper bound on the amount of measurement dependence that can be present, whenever this amount was less than the lower bound on the amount needed to explain the observed violation of a Bell inequality in a classical causal model, one could infer that these violations were due to nonclassical effects
Summary
Bell’s theorem [1] can arguably be seen as the most radical departure from classical physics. By considering a slight modification of a Bell experiment, one had the means of determining an upper bound on the amount of measurement dependence that can be present, whenever this amount was less than the lower bound on the amount needed to explain the observed violation of a Bell inequality in a classical causal model, one could infer that these violations were due to nonclassical effects. As compared with usual Bell scenarios, these new networks have two characteristic features: first, the fact that the correlations between the distant parties are mediated by a number of independent sources; and, second, the fact that one can prove nonclassical behavior even without the need for any inputs, something considered quintessential in Bell’s theorem [37]. VI, we discuss our results and point out interesting directions for future research
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