Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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


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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.


  1. Bell, J. S. On the Einstein Podolvski Rosen paradox. Physics (N.Y.) 1, 195–200 (1965).

    Google Scholar 

  2. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).

    Article  ADS  Google Scholar 

  3. Aspect, A., Grangier, P. & Roger, G. Experimental realization of Einstein–Podolsky–Rosen–Bohm gedanken experiment: A new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982).

    Article  ADS  Google Scholar 

  4. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  5. Leggett, A. J. & Garg, A. Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54, 857–860 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  6. Ruskov, R., Korotkov, A. N. & Mizel, A. Signatures of quantum behavior in single-qubit weak measurements. Phys. Rev. Lett. 96, 200404 (2006).

    Article  ADS  Google Scholar 

  7. Goggin, M. E. et al. Violation of the Leggett–Garg inequality with weak measurement of photons. Preprint at (2009).

  8. Xu, J. S., Li, C. F., Zou, X. B. & Guo, G. C. Experimentally identifying the transition from quantum to classical with Leggett–Garg inequalities. Preprint at (2009).

  9. Korotkov, A. N. & Averin, D. V. Continuous weak measurement of quantum coherent oscillations. Phys. Rev. B 64, 165310 (2001).

    Article  ADS  Google Scholar 

  10. Ruskov, R. & Korotkov, A. N. Quantum feedback control of a solid-state qubit. Phys. Rev. B 66, 041401 (2002).

    Article  ADS  Google Scholar 

  11. Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009).

    Article  ADS  Google Scholar 

  12. Chow, J. M. et al. Entanglement metrology using a joint readout of superconducting qubits. Preprint at (2009).

  13. Blais, A., Huang, R., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys. Rev. A 69, 062320 (2004).

    Article  ADS  Google Scholar 

  14. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    Article  ADS  Google Scholar 

  15. Leggett, A. J. Testing the limits of quantum mechanics: Motivation, state of play, prospects. J. Phys. Condens. Matter 14, R415–R451 (2002).

    Article  ADS  Google Scholar 

  16. Leggett, A. J. Realism and the physical world. Rep. Prog. Phys. 71, 022001-6 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  17. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article  ADS  Google Scholar 

  18. Schreier, J. A. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502 (2008).

    Article  ADS  Google Scholar 

  19. Gambetta, J. et al. Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect. Phys. Rev. A 77, 012112 (2008).

    Article  ADS  Google Scholar 

  20. Schuster, D. I. et al. Ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. Phys. Rev. Lett. 94, 123602 (2004).

    Article  ADS  Google Scholar 

  21. Misra, B. & Sudarshan, E. C. G. The Zeno’s paradox in quantum theory. J. Math. Phys. Sci. 18, 756–763 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  22. Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. Quantum Zeno effect. Phys. Rev. A 41, 2295–2300 (1990).

    Article  ADS  Google Scholar 

  23. Bernu, J. et al. Freezing coherent field growth in a cavity by the quantum Zeno effect. Phys. Rev. Lett. 101, 180402 (2008).

    Article  ADS  Google Scholar 

  24. Goan, H. S. & Milburn, G. J. Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement. Phys. Rev. B 64, 235307 (2001).

    Article  ADS  Google Scholar 

  25. Shnirman, A., Mozyrsky, D. & Martin, I. Output spectrum of a measuring device at arbitrary voltage and temperature. Europhys. Lett. 67, 840–846 (2004).

    Article  ADS  Google Scholar 

  26. Torrey, H. C. Transient nutations in nuclear magnetic resonance. Phys. Rev. 76, 1059–1068 (1947).

    Article  ADS  Google Scholar 

  27. Il’ichev, E. et al. Continuous monitoring of Rabi oscillations in a Josephson flux qubit. Phys. Rev. Lett. 91, 097906 (2003).

    Article  ADS  Google Scholar 

  28. Deblock, R., Onac, E., Gurevich, L. & Kouwenhoven, L. P. Detection of quantum noise from an electrically driven two-level system. Science 301, 203–206 (2003).

    Article  ADS  Google Scholar 

  29. Manassen, Y., Hamers, R. J., Demuth, J. E. & Castellano, A. J. Jr Direct observation of the precession of individual paramagnetic spins on oxidized silicon surfaces. Phys. Rev. Lett. 62, 2531–2534 (1989).

    Article  ADS  Google Scholar 

  30. Castellanos-Beltran, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 929–931 (2008).

    Article  ADS  Google Scholar 

  31. Bergeal, N. et al. Analog information processing at the quantum limit with a Josephson ring modulator. Nature Phys. 6, 296–302 (2010).

    Article  ADS  Google Scholar 

Download references


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.

Author information

Authors and Affiliations



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.

Corresponding author

Correspondence to Patrice Bertet.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1213 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing