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Chinese Physics Letters

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

周清平, 方卯发, 刘小娟

Published Jan 1, 2005• 0 citations
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Abstract

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.

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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.
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 γ αβ of the two coherent displacements being opposite to the internal phase shift ϕ of the beam splitter (γ αβ = −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 γ αβ . 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.
Quantum entanglement and quantum nonlocality of N -photon entangled states |ψ Nm ⟩ = C m [cos γ| N − m ⟩ 1 | m ⟩ 2 +e iθ m sin γ| m ⟩ 1 | N − m ⟩ 2 ] and their superpositions are studied. We point out that the relative phase θ m affects the quantum nonlocality but not the quantum entanglement for the state |ψ Nm ⟩. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |ψ Nm ⟩, superposition coefficients and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |ψ Nm ⟩ can increase the amount of entanglement and give more ways to reach the maximal violation of the Bell inequality.
Entanglement does not always require one particle per party. It was predicted some thirty years ago that a single photon traversing a beam splitter could violate a Bell inequality. Although initially debated, single-photon nonlocality was eventually demonstrated via homodyne measurements. Here, we present an alternate realisation that avoids the complexity of homodyne measurements and potential loopholes in their implementation. We violate a Bell inequality by performing joint measurements on two copies of the same single-photon entangled state, where one photon acts as a phase reference for the other, making it self-referential. We observe CHSH parameters of 2.71±0.092.71\pm 0.092.71±0.09 and 2.23±0.072.23\pm 0.072.23±0.07, depending on the joint measurements implemented. This offers a new perspective on single-photon nonlocality and a more accessible experimental route, potentially applicable to general mode-entangled states in diverse platforms.
Different degrees of freedom of single photons have been entangled and are used as a resource for various quantum technology applications. We present a simple scheme to perform Bell's test and show the violation of CHSH inequality in a path-entangled single photon state using interferometric and its equivalent non-interferometric approach in beam splitter setting. We demonstrate this experimentally by generating and controlling path-entangled state using both, heralded and un-heralded single photons from spontaneous parametric down-conversion. The experimental results we present show the transition to violation of CHSH inequality when the purity of single photons state visibility increase above 70\% , P>0.7\mathcal{P} > 0.7P>0.7. Our procedure using single beam splitter and two detector module for un-heralded single photon source allows a simple way to test for purity of any single photon source and to study quantum correlations on systems driven by dynamics where single particle entanglement with position space is prominent.
We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between two measurement settings, with each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the four total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test the robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes.