On the rank of two-dimensional simplicial distributions

Year 2024, Early Access, 1 - 22

Cihan Okay

https://doi.org/10.15672/hujms.1414442

Abstract

Simplicial distributions provide a framework for studying quantum contextuality, a generalization of
Bell’s non-locality. Understanding extremal simplicial distributions is of fundamental importance with
applications to quantum computing. We introduce a rank formula for twisted simplicial distributions
defined for 2-dimensional measurement spaces and provide a systematic approach for describing extremal
distributions.

Keywords

simplicial sets, quantum contextuality, simplicial distributions, graph theory

Supporting Institution

US Air Force Office of Scientific Research

Project Number

FA9550-21-1-0002

References

• [1] S. Abramsky and A. Brandenburger, The sheaf-theoretic structure of non-locality and contextuality, New J. Phys. 13 (11), 113036, 2011.