Manipulation of Quantum Nonlocality of the Single-Photon Entangled State via Beam Splitter

Quantum nonlocality of the single-photon entangled state emerging from a beam splitter with arbitrary controlling parameters is investigated by means of the parity measurement. The condition of the maximal violation of the Bell-CHSH inequality is obtained for the single-photon entangled state. Under the condition of the small coherent intensity J(J=0.1) and the phase difference γαβ of the two coherent displacements being opposite to the internal phase shift φ of the beam splitter (γαβ=-φ), we find that the quantum nonlocality depends only on the reflection coefficient R of the beam splitter, while φ plays an important role for selecting γαβ. The strongest quantum nonlocality can be observed for a 50:50 beam splitter. If R deviates from the intermediate value 0.5, the quantum nonlocality decreases gradually, even vanishes. Our results provide a method to observe and manipulate the quantum nonlocality of the single-photon entangled state by adjusting the parameters of the coherent displacements and the beam splitter.