Extremal simplicial distributions on cycle scenarios with arbitrary outcomes

• URL: http://arxiv.org/abs/2406.19961v1
• Date: Fri, 28 Jun 2024 14:48:31 GMT
• Title: Extremal simplicial distributions on cycle scenarios with arbitrary outcomes
• Authors: Aziz Kharoof, Cihan Okay, Selman Ipek,
• Abstract summary: Cycle scenarios are a significant class of contextuality scenarios, with the Clauser-Horne-Shimony-Holt (CHSH) scenario being a notable example. We employ homotopical methods in the framework of simplicial distributions to characterize all contextual vertices of the non-signaling polytope corresponding to cycle scenarios with arbitrary outcomes. This enables us to extend beyond scenarios formed by gluing cycle scenarios and describe contextual extremal simplicial distributions in these generalized contexts.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Cycle scenarios are a significant class of contextuality scenarios, with the Clauser-Horne-Shimony-Holt (CHSH) scenario being a notable example. While binary outcome measurements in these scenarios are well understood, the generalization to arbitrary outcomes remains less explored, except in specific cases. In this work, we employ homotopical methods in the framework of simplicial distributions to characterize all contextual vertices of the non-signaling polytope corresponding to cycle scenarios with arbitrary outcomes. Additionally, our techniques utilize the bundle perspective on contextuality and the decomposition of measurement spaces. This enables us to extend beyond scenarios formed by gluing cycle scenarios and describe contextual extremal simplicial distributions in these generalized contexts.

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