Certifying Randomness or its Lack Thereof for General Network Scenarios

Abstract: The certification of intrinsic randomness is foundational to quantum information theory and central in many practical applications thereof, such as in the generation of unquestionably random numbers and in cryptographic protocols. Device-independent randomness certification based on violations of Bell inequalities has been thoroughly investigated within the standard Bell scenario. In this work, we aim to extend this line of research by exploring randomness certification in more general causal structures, namely, network scenarios. To address this task, we demonstrate how the computational tool known as the inflation technique can be adapted. As proof of concept, we use inflation to certify randomness relative to a beyond-quantum adversary for sample probability distributions obtained in the bilocality and triangle scenarios. Complementarily, we also provide computational methods for the problem of certifying an absence of randomness, which should not be conflated with certifying the classicality of a given probability distribution. We conclude with a discussion of conceptual subtleties regarding randomness certification in networks, highlighting important open problems in this nascent research field.