Exclusivity Graph Approach to Instrumental Inequalities

Instrumental variables allow the estimationof cause and effect relations even in pres-ence of unobserved latent factors, thus provid-ing a powerful tool for any science whereincausal inference plays an important role.More recently, the instrumental scenario hasalso attracted increasing attention in quantumphysics, since it is related to the seminal Bell’stheorem and in fact allows the detection ofeven stronger quantum effects, thus enhancingour current capabilities to process informationand becoming a valuable tool in quantum cryp-tography. In this work, we further explore thisbridge between causality and quantum theoryand apply a technique, originally developed inthe field of quantum foundations, to expressthe constraints implied by causal relations inthe language of graph theory. This new ap-proach can be applied to any causal model con-taining a latent variable. Here, by focusing onthe instrumental scenario, it allows us to easilyreproduce known results as well as obtain newones and gain new insights on the connectionsand differences between the instrumental andthe Bell scenarios.

Davide Poderini, Rafael Chaves, Iris Agresti, Gonzalo Carvacho, Fabio Sciarrino

The work has been published in the Proceedings of the “Conference on Uncertainty in Artificial Intelligence” held in Tel-Aviv, Israel.

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