Two-Source Topological Phases and A New Method for Testing Bell-CHSH Inequalities

Quantum topological phases arise under the influence of vector potential or vector potential-like physical quantities that enter as a complex phase factor into the wave functions of particles moving along closed trajectories around singularities created by using electric or magnetic field sources, without the effects of any classical force. The well-known examples of the topological phases are the Aharonov-Bohm (AB) and Aharonov-Casher (AC) physical processes. The effects of topological phases on entangled quantum mechanical systems are of great importance for revealing the non-local properties of quantum mechanics. In this regard, the joint probabilities of particle arrival at each of two spatially separated detectors for momentum-correlated states can be calculated by considering two-source AB and AC systems in EPR-Bohm type hybrid gedanken experimental setups. From this point of view, in this work, the effect of topological phases on quantum entangled states will be investigated and it will be shown that the system to be designed using beam splitters and phase retarders can be used as an analog for joint spin measurements within the framework of entirely quantum mechanics. As a result, this setup will be proposed as a new experimental method for testing the Bell-CHSH inequalities.