Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards an Entanglement-Sensitive Langlands Correspondence

TL;DR

This paper explores the deep connections between quantum entanglement, topological matter, and advanced mathematical frameworks like the Langlands program, aiming to develop an entanglement-sensitive correspondence with both theoretical and numerical insights.

Contribution

It extends the theoretical framework linking quantum entanglement with geometric Langlands concepts and validates these ideas through simulations and condensed matter physics perspectives.

Findings

Entanglement acts as a cohomological obstruction in global state reconstruction.

Connections between sheafification, Hecke modifications, and topological matter are established.

Numerical simulations support the theoretical extensions.

Abstract

Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to global-from-local signatures while acting faithfully with respect to within-patch multipartite structures. Nontrivial connections to Hecke modifications and the geometric Langlands program are explored in the process. The aim of this work is to validate and extend a number of the claims made in [arXiv:2511.04326] through both theoretical analysis and numerical simulations, employing concrete perspectives from condensed matter physics.