Certifying Randomness or its Lack Thereof for General Network Scenarios

TL;DR

This paper extends the certification of intrinsic randomness from standard Bell scenarios to complex network scenarios using the inflation technique, demonstrating its effectiveness in certifying randomness and non-randomness in quantum networks.

Contribution

It adapts the inflation technique for randomness certification in network scenarios and provides computational methods for certifying both randomness and its absence.

Findings

Successfully certifies randomness in bilocality and triangle scenarios.

Provides methods to certify the absence of randomness.

Highlights open problems in network-based randomness certification.

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.