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arXiv:quant-ph/0504084 · Physical Review A

Generating optimal states for a homodyne Bell test

Sonja Daffer, P. L. Knight

Published Sep 1, 2005• 10 citations
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Abstract

We present a scheme that produces a conditionally prepared state that can be used for a Bell test based on homodyne detection. The state is near optimal for Bell-inequality violations based on quadrature-phase homodyne measurements that use correlated photon-number states. The scheme utilizes a Gaussian entanglement distillation protocol and uses only beam splitters and photodetection to conditionally prepare a non-Gaussian state from a source of two-mode squeezed states with low squeezing parameter.

DOI
10.1103/physreva.72.034101

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We present a scheme that produces a conditionally prepared state that can be used for a Bell test based on homodyne detection. The state is near optimal for Bell-inequality violations based on quadrature-phase homodyne measurements that use correlated photon-number states. The scheme utilizes a Gaussian entanglement distillation protocol and uses only beam splitters and photodetection to conditionally prepare a non-Gaussian state from a source of two-mode squeezed states with low squeezing parameter.
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We propose a feasible optical setup allowing for a loophole‐free Bell test with efficient homodyne detection. A non‐Gaussian entangled state is generated from a two‐mode squeezed vacuum by subtracting a single photon from each mode, using beam splitters and standard low‐efficiency single‐photon detectors. A Bell violation exceeding 1% is achievable with 6 dB of squeezing, a photodetector efficiency around 10%, and an homodyne efficiency around 95%. A feasibility analysis, based upon the recent generation of single‐mode non‐Gaussian states via photon subtraction, suggests that this method opens a promising avenue towards a complete experimental Bell test.
We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality violation using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-Gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the tolerance of the achievable Bell violation in the various experimentally relevant parameters such as the detector efficiencies, the electronic noise, the mixedness of the initial Gaussian state, and the probability of false triggers. We also consider several alternative schemes involving squeezed states, linear optical elements, conditional photon subtraction, and homodyne detection.
When separated measurements on entangled quantum systems are performed, the theory predicts correlations that cannot be explained by any classical mechanism: communication is excluded because the signal should travel faster than light; preestablished agreement is excluded because Bell inequalities are violated. All optical demonstrations of such violations have involved discrete degrees of freedom and are plagued by the detection-efficiency loophole. A promising alternative is to use continuous variables combined with highly efficient homodyne measurements. However, all the schemes proposed so far use states or measurements that are extremely difficult to achieve, or they produce very weak violations. We present a simple method to generate large violations for feasible states using both photon counting and homodyne detections. The present scheme can also be used to obtain nonlocality from easy-to-prepare Gaussian states (e.g., two-mode squeezed state).