Connecting extended Wigner's friend arguments and noncontextuality

TL;DR

This paper explores the deep connections between Local Friendliness scenarios and Kochen-Specker noncontextuality, deriving new inequalities and showing their equivalence in certain quantum scenarios, advancing understanding of quantum reality constraints.

Contribution

It establishes a formal link between Local Friendliness and Kochen-Specker noncontextuality, deriving new inequalities and translating contextuality arguments into Local Friendliness proofs.

Findings

Derived new Local Friendliness inequalities from Kochen-Specker results

Proved the equivalence of the Local Friendliness and Bell polytopes in certain scenarios

Translated Kochen-Specker contextuality arguments into Local Friendliness no-go theorems

Abstract

The Local Friendliness argument is an extended Wigner's friend no-go theorem that provides strong constraints on the nature of reality -- stronger even than those imposed by Bell's theorem or by noncontextuality arguments. In this work, we prove a variety of connections between Local Friendliness scenarios and Kochen-Specker noncontextuality. Specifically, we first show how one can derive new Local Friendliness inequalities using known tools and results from the literature on Kochen-Specker noncontextuality. In doing so, we provide a new derivation for some of the facets of the Local Friendliness polytope, and we prove that this polytope is equal to the Bell polytope in a wide range of extended Wigner's friend scenarios with multipartite agents and sequential measurements. We then show how any possibilistic Kochen-Specker argument can be mathematically translated into a related proof of the Local Friendliness no-go theorem. In particular, we construct a novel kind of Local Friendliness scenario where a friend implements several compatible measurements (or joint measurements of these) in between the superobserver's operations on them. We illustrate this with the well-known 5-cycle and Peres-Mermin contextuality arguments.