It from qubit: how to draw quantum contextuality

TL;DR

This paper explores the use of Grothendieck's dessins d'enfants to understand quantum contextuality and measurement in qubits, linking finite geometries with topological and algebraic structures.

Contribution

It introduces a novel approach employing dessins d'enfants to analyze quantum measurement acts and contextuality in qubits, advancing the conceptual framework.

Findings

Reveals topological structures underlying quantum measurement

Links finite geometries with algebraic topology in quantum context

Provides new insights into quantum non-locality and contextuality

Abstract

Wheeler's {\it observer-participancy} and the related {\it it from bit} credo refer to quantum non-locality and contextuality. The mystery of these concepts slightly starts unveiling if one encodes the (in)compatibilities between qubit observables in the relevant finite geometries. The main objective of this treatise is to outline another conceptual step forward by employing Grothendieck's {\it dessins d'enfants} to reveal the topological and (non)algebraic machinery underlying the measurement acts and their information content.