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Experimental violation of a Bell’s inequality in time with weak measurement

Abstract

The violation of Bell inequalities with two entangled and spatially separated quantum two-level systems (TLSs) is often considered as the most prominent demonstration that nature does not obey local realism. Under different but related assumptions of macrorealism—which macroscopic systems plausibly fulfil—Leggett and Garg derived a similar inequality for a single degree of freedom undergoing coherent oscillations and being measured at successive times. Here, we test such a ‘Bell’s inequality in time’, which should be violated by a quantum TLS. Our TLS is a superconducting quantum circuit in which Rabi oscillations are continuously driven while it is continuously and weakly measured. The time correlations present at the detector output agree with quantum-mechanical predictions and violate the Leggett–Garg inequality by five standard deviations.

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Figure 1: Comparison between two thought experiments that test the usual CHSH Bell’s inequality and the Bell’s inequality in time.
Figure 2: Experimental implementation of the thought experiment in Fig. 1b with a quantum electrical circuit.
Figure 3: Continuous monitoring of the driven TLS at different Rabi frequencies ωR and measurement strengths .
Figure 4: Experimental violation of the ‘Bell’s inequality in time’ introduced in Fig. 1b.

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Acknowledgements

We acknowledge financial support from European projects EuroSQIP and SCOPE, and from ANR project Quantjo and C’Nano Ile-de-France for the nanofabrication facility at SPEC. We thank P. Sénat, P. Orfila, J-C. Tack and D. Bouville for technical support, and acknowledge useful discussions within the Quantronics group and with A. Lupascu, A. Wallraff, M. Devoret and R. Ruskov.

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Contributions

A.N.K., P.B. and A.P-L. did the theoretical work, A.P-L., F.M., P.B., D.V. and D.E. designed the experiment, A.P-L. fabricated the sample, A.P-L., F.M., P.B. and F.N. carried out the measurements, A.P-L., F.M., D.V. and P.B. analysed the data, and all of the authors contributed to the writing of the manuscript.

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Correspondence to Patrice Bertet.

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The authors declare no competing financial interests.

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Palacios-Laloy, A., Mallet, F., Nguyen, F. et al. Experimental violation of a Bell’s inequality in time with weak measurement. Nature Phys 6, 442–447 (2010). https://doi.org/10.1038/nphys1641

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