Estimating the volumes of correlations sets in causal networks

• URL: http://arxiv.org/abs/2311.08574v1
• Date: Tue, 14 Nov 2023 22:35:57 GMT
• Title: Estimating the volumes of correlations sets in causal networks
• Authors: Giulio Camillo, Pedro Lauand, Davide Poderini, Rafael Rabelo, Rafael Chaves
• Abstract summary: Causal networks beyond that in paradigmatic Bell's theorem can lead to new kinds and applications of non-classicality. We show where the most disseminated tool in the community, is unable to detect a significant portion of the non-classical behaviors. We also show that the use interventions, a central tool in inference, can substantially our ability to witness non-classicality.
• Score: 0.41942958779358674
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Causal networks beyond that in the paradigmatic Bell's theorem can lead to new kinds and applications of non-classical behavior. Their study, however, has been hindered by the fact that they define a non-convex set of correlations and only very incomplete or approximated descriptions have been obtained so far, even for the simplest scenarios. Here, we take a different stance on the problem and consider the relative volume of classical or non-classical correlations a given network gives rise to. Among many other results, we show instances where the inflation technique, arguably the most disseminated tool in the community, is unable to detect a significant portion of the non-classical behaviors. Interestingly, we also show that the use of interventions, a central tool in causal inference, can enhance substantially our ability to witness non-classicality.

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