Berry Phase in Pathangled Systems

TL;DR

This paper introduces pathangled quantum states and demonstrates how Berry phases and production angles can be used to control entanglement geometrically, revealing a critical angle related to Bell correlations.

Contribution

It presents a novel framework using pathangled states and adiabatic evolution to manipulate entanglement and Bell correlations through geometric phases.

Findings

Identifies a critical angle of approximately 24.97° for Bell-limit manifestation.

Shows that Berry phases serve as additional degrees of freedom for entanglement control.

Provides a simplified method for state preparation with geometry-driven entanglement manipulation.

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.