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arXiv:1012.1916 · Physical Review A

Large violation of Bell inequalities using both particle andwave measurements

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

Published Aug 8, 2011• 38 citations
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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; 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).

DOI
10.1103/physreva.84.022105

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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; 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).
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.
It is a long-standing belief, as pointed out by Bell in 1986, that it is impossible to use a two-mode Gaussian state possessing a positive-definite Wigner function to demonstrate nonlocality as the Wigner function itself provides a local hidden-variable model. In particular, when one performs continuous-variable (CV) quadrature measurements upon a routinely generated CV entanglement, namely, the two-mode squeezed vacuum (TMSV) state, the resulting Wigner function is positive-definite and as such, the TMSV state cannot violate any Bell inequality using CV quadrature measurements. We show here, however, that a Bell inequality for CV states in terms of entropies can be quantum mechanically violated by the TMSV state with two coarse-grained quadrature measurements per site within experimentally accessible parameter regime. The proposed CV entropic Bell inequality is advantageous for an experimental test, especially for a possible loophole-free test of nonlocality, as the quadrature measurements can be implemented with homodyne detections of nearly 100100%100 detection efficiency under current technology.
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.
Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.
We have theoretically investigated the possibility of using any of several continuous-variable Bell-type inequalities---for which the dichotomic measurements are achieved with coarse-grained quadrature (homodyne) measurements---in a multiparty configuration where each participant is given a section, in the frequency domain, of the output of an optical parametric oscillator which has been synchronously pumped with a frequency comb. Such light sources are undergoing intense study due to their novel properties, including the potential for production of light entangled in many hundreds of physical modes---a critical component for many proposals in optical or hybrid-optical quantum computation proposals. The situation we study notably uses only highly efficient optical homodyne detection, meaning that in such systems the fair-sampling loophole would be relatively easy to avoid.