Berry Phase in Pathangled Systems

Abstract

We introduce pathangled quantum states, spatially correlated systems governed via production angles, to achieve geometric control of entanglement beyond spin/polarization constraints. By driving the system through cyclic adiabatic evolution of an external parameter in Mach-Zehnder interferometers, we demonstrate that Berry phases and production angles become additional degrees of freedom for Bell correlations. We identify an approximate critical angle $24.97^{\circ }$ that geometrically manifests the Bell-limit for certain measurement settings, delineating boundaries between local-hidden-variable theories and quantum mechanics. This framework simplifies state preparation while enabling geometry-driven entanglement control, thus providing distinct experimental advantages.

5 Pages, 2 Figures