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Violation of Bell's inequality in Josephson phase qubits


The measurement process plays an awkward role in quantum mechanics, because measurement forces a system to ‘choose’ between possible outcomes in a fundamentally unpredictable manner. Therefore, hidden classical processes have been considered as possibly predetermining measurement outcomes while preserving their statistical distributions1. However, a quantitative measure that can distinguish classically determined correlations from stronger quantum correlations exists in the form of the Bell inequalities, measurements of which provide strong experimental evidence that quantum mechanics provides a complete description2,3,4. Here we demonstrate the violation of a Bell inequality in a solid-state system. We use a pair of Josephson phase qubits5,6,7 acting as spin-1/2 particles, and show that the qubits can be entangled8,9 and measured so as to violate the Clauser–Horne–Shimony–Holt (CHSH) version of the Bell inequality10. We measure a Bell signal of 2.0732 ± 0.0003, exceeding the maximum amplitude of 2 for a classical system by 244 standard deviations. In the experiment, we deterministically generate the entangled state, and measure both qubits in a single-shot manner, closing the detection loophole11. Because the Bell inequality was designed to test for non-classical behaviour without assuming the applicability of quantum mechanics to the system in question, this experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system7.

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Figure 1: Resonator-coupled qubits.
Figure 2: Entanglement analysis.
Figure 3: Verification experiments.
Figure 4: Entanglement analysis.


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We thank A. Korotkov and A. Kofman for discussions of our measurement process. Devices were made at the UCSB Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network. This work was supported by IARPA under grant W911NF-04-1-0204 and by the NSF under grant CCF-0507227.

Author Contributions M.A. performed the experiment and analysed the data, while H.W. fabricated the sample. J.M.M. and E.L. designed the custom electronics and M.H. developed the calibrations for it. M.A. and M.N. provided software infrastructure. All authors contributed to various tasks, such as the fabrication process, qubit design, or experimental set-up.

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Correspondence to John M. Martinis.

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This file contains Supplementary Methods, Supplementary Data, Supplementary Figures 1-2 with Legends and Supplementary References. Supplementary Tables II and II were corrected on 24 December 2009. (PDF 387 kb)

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Ansmann, M., Wang, H., Bialczak, R. et al. Violation of Bell's inequality in Josephson phase qubits. Nature 461, 504–506 (2009).

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