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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Large violation of Bell inequalities using both particle and wave measurements

Daniel Cavalcanti, Nicolas Brunner, Paul Skrzypczyk, Alejo Salles, Valerio Scarani

Published May 1, 2011• 4 citations
Publisher

Abstract

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; pre-established 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 schemes proposed so far use states or measurements that are extremely difficult to achieve, or produce very weak violations. Here we show that large violations for feasible states can be achieved if both photon counting and homodyne detections are used. Our scheme may lead to the first violation of Bell inequalities using continuous-variable measurements and pave the way for a loophole-free Bell test.

DOI
10.1109/cleoe.2011.5943443

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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; pre-established 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 schemes proposed so far use states or measurements that are extremely difficult to achieve, or produce very weak violations. Here we show that large violations for feasible states can be achieved if both photon counting and homodyne detections are used. Our scheme may lead to the first violation of Bell inequalities using continuous-variable measurements and pave the way for a loophole-free Bell test.
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).
A Bell inequality is a fundamental test to rule out local hidden variable model descriptions of correlations between two physically separated systems. There have been a number of experiments in which a Bell inequality has been violated using discrete-variable systems. We demonstrate a violation of Bell's inequality using continuous variable quadrature measurements. By creating a four-mode entangled state with homodyne detection, we recorded a clear violation with a Bell value of B=2.31±0.02. This opens new possibilities for using continuous variable states for device independent quantum protocols.
It is shown that a loophole-free Bell test can be achieved using continuous variables of light. A feasible optical setup is proposed for this purpose, based on a non-Gaussian state of light and high-efficiency homodyne detectors. The non-Gaussian entangled state can be generated from a two-mode squeezed vacuum state by subtracting a single photon from each mode using beam splitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% can be attained with 6 dB squeezed light and an homodyne efficiency around 95%. A detailed feasibility analysis, including the effect of the detector efficiency, the electronic noise, the impurity of the non-Gaussian state, and the probability of false triggers, suggests that this method opens a promising avenue towards a complete experimental Bell test.
We propose a whole family of physical states that yield a maximal violation of Bell inequalities, when using quadrature-phase homodyne detection. This result is based on a binning process called root binning, that is used to transform the continuous-variable measurements into binary results needed for the tests of quantum mechanics versus local realistic theories. A physical process in order to produce such states is also suggested. The use of high-efficiency spacelike separated homodyne detections with these states and this binning process would result in a conclusive loophole-free test of quantum mechanics.
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 squeezed light and a homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent experimental generation of single-mode non-Gaussian states, suggests that this method opens a promising avenue towards a complete experimental Bell test.