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Abstract This paper examines networks ofnmeasuring parties sharingmnonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources possibly depending on outputs of earlier-measured ones. A specific framework is provided for studying probability distributions arising in such networks, and this framework is used to directly prove some accepted, but often only implicitly invoked, facts: there is a uniquely determined and well-defined joint probability distribution for the outputs of all resources shared by the parties, and this joint distribution is nonsignaling. It is furthermore shown that is often sufficient to restrict consideration to only extremal nonsignaling resources when considering features and properties of such networks. Finally, the framework illustrates how the physical theory of nonsignaling boxes and local wirings iscausal, supporting the applicability of the inflation technique to constrain such models. For an application, we probe the example of $(3,2,2)$inequalities that witness genuine three-party nonlocality according to the local-operations-shared-randomness definition, and show how all other examples can be derived from that of Maoet al(2022Phys. Rev. Lett.129150401). 

The probability estimation framework involves direct estimation of the probability of occurrences of outcomes conditioned on measurement settings and side information. It is a powerful tool for certifying randomness in quantum nonlocality experiments. In this paper, we present a self-contained proof of the asymptotic optimality of the method. Our approach refines earlier results to allow a better characterisation of optimal adversarial attacks on the protocol. We apply these results to the (2,2,2) Bell scenario, obtaining an analytic characterisation of the optimal adversarial attacks bound by no-signalling principles, while also demonstrating the asymptotic robustness of the PEF method to deviations from expected experimental behaviour. We also study extensions of the analysis to quantum-limited adversaries in the (2,2,2) Bell scenario and no-signalling adversaries in higher (n,m,k) Bell scenarios. 

Abstract We classify the extreme points of a polytope of probability distributions in the (2,2,2) CHSH-Bell setting that is induced by a single Tsirelson bound. We do the same for a class of polytopes obtained from a parametrized family of multiple Tsirelson bounds interacting non-trivially. Such constructions can be applied to device-independent random number generation using the method of probability estimation factors (2018 Phys. Rev. A98040304(R)). We demonstrate a meaningful improvement in certified randomness applying the new polytopes characterized here.