Topological Contextuality and Quantum Representations

TL;DR

This paper explores how topological and algebraic structures in quantum systems reveal contextuality, demonstrating that certain braid group representations inherently violate classical noncontextuality assumptions, with implications for quantum computation.

Contribution

It provides a rigorous topological framework linking braid group representations to quantum contextuality, especially in SU(2) and Fibonacci models, advancing understanding of quantum resources.

Findings

Braid group representations induce state-dependent contextuality.

Explicit construction of unitary representations on fusion spaces.

Topological framework classifies and quantifies contextuality.

Abstract

Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid group representations induced by modular categories, particularly those associated with SU(2) at level k and Fibonacci anyon models, exhibit state-dependent contextuality characterized by violations of noncontextuality inequalities. By explicitly constructing these unitary representations on fusion spaces, the study establishes a direct correspondence between braiding operations and logical contextuality scenarios. The results offer a comprehensive topological framework to classify and quantify contextuality in low-dimensional quantum systems, elucidating its role as a resource in topological quantum computation and advancing the interface between quantum algebra, topology, and quantum foundations.