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.

Violating Bell’s inequality with remotely connected superconducting qubits


Quantum communication relies on the efficient generation of entanglement between remote quantum nodes, as entanglement is required to achieve and verify secure communications1. Remote entanglement has been realized using a number of different probabilistic schemes2,3, but deterministic remote entanglement has only been demonstrated recently, using a variety of superconducting circuit approaches4,5,6. However, the deterministic violation of a Bell inequality7, a strong measure of quantum correlation, has not been demonstrated so far in a superconducting quantum communication architecture, in part because achieving sufficiently strong correlation requires fast and accurate control of the emission and capture of the entangling photons. Here, we present a simple and robust architecture for achieving this benchmark result in a superconducting system.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Device description.
Fig. 2: State transfer, remote entanglement and Bell violation using the relay method.
Fig. 3: Single qubit ‘ping-pong’ with itinerant photons.
Fig. 4: State transfer, remote entanglement and Bell violation using itinerant photons.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. Cirac, J. I., Zoller, P., Kimble, H. J. & Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997).

    ADS  Article  Google Scholar 

  2. Narla, A. et al. Robust concurrent remote entanglement between two superconducting qubits. Phys. Rev. X 6, 031036 (2016).

    Google Scholar 

  3. Dickel, C. et al. Chip-to-chip entanglement of transmon qubits using engineered measurement fields. Phys. Rev. B 97, 064508 (2018).

    ADS  Article  Google Scholar 

  4. Kurpiers, P. et al. Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 558, 264–267 (2018).

    ADS  Article  Google Scholar 

  5. Axline, C. J. et al. On-demand quantum state transfer and entanglement between remote microwave cavity memories. Nat. Phys. 14, 705–710 (2018).

    Article  Google Scholar 

  6. Campagne-Ibarcq, P. et al. Deterministic remote entanglement of superconducting circuits through microwave two-photon transitions. Phys. Rev. Lett. 120, 200501 (2018).

    ADS  Article  Google Scholar 

  7. Bell, J. S. On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964).

    MathSciNet  Article  Google Scholar 

  8. Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).

    ADS  Article  Google Scholar 

  9. Kelly, J. et al. State preservation by repetitive error detection in a superconducting quantum circuit. Nature 519, 66–69 (2015).

    ADS  Article  Google Scholar 

  10. Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009).

    ADS  Article  Google Scholar 

  11. Vlastakis, B. et al. Deterministically encoding quantum information using 100-photon Schrödinger cat states. Science 342, 607–610 (2013).

    ADS  MathSciNet  Article  Google Scholar 

  12. O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).

    ADS  Article  Google Scholar 

  13. Chu, Y. et al. Quantum acoustics with superconducting qubits. Science 358, 199–202 (2017).

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  16. Palacios-Laloy, A. et al. Experimental violation of a Bell’s inequality in time with weak measurement. Nat. Phys. 6, 442–447 (2010).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  18. Chen, Y. et al. Qubit architecture with high coherence and fast tunable coupling. Phys. Rev. Lett. 113, 220502 (2014).

    ADS  Article  Google Scholar 

  19. Fowler, A. G. et al. Surface code quantum communication. Phys. Rev. Lett. 104, 180503 (2010).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  21. Barends, R. et al. Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013).

    ADS  Article  Google Scholar 

  22. Sillanpää, M. A., Park, J. I. & Simmonds, R. W. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007).

    ADS  Article  Google Scholar 

  23. Neeley, M. et al. Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state. Nat. Phys. 4, 523–526 (2008).

    Article  Google Scholar 

  24. Leung, N. et al. Deterministic bidirectional communication and remote entanglement generation between superconducting qubits. NPJ Quantum Inf. 5, 18 (2019).

    ADS  Article  Google Scholar 

  25. Steffen, M. et al. State tomography of capacitively shunted phase qubits with high fidelity. Phys. Rev. Lett. 97, 050502 (2006).

    ADS  Article  Google Scholar 

  26. Garg, A. & Mermin, N. D. Detector inefficiencies in the Einstein–Podolsky–Rosen experiment. Phys. Rev. D 35, 3831–3835 (1987).

    ADS  Article  Google Scholar 

  27. Korotkov, A. N. Flying microwave qubits with nearly perfect transfer efficiency. Phys. Rev. B 84, 014510 (2011).

    ADS  Article  Google Scholar 

  28. Pechal, M. et al. Microwave-controlled generation of shaped single photons in circuit quantum electrodynamics. Phys. Rev. X 4, 041010 (2014).

    Google Scholar 

  29. Sete, E. A., Mlinar, E. & Korotkov, A. N. Robust quantum state transfer using tunable couplers. Phys. Rev. B 91, 144509 (2015).

    ADS  Article  Google Scholar 

  30. Kelly, J. S. Fault-Tolerant Superconducting Qubits. PhD thesis, Univ. California, Santa Barbara (2015).

  31. Dunsworth, A. et al. A method for building low loss multi-layer wiring for superconducting microwave devices. Appl. Phys. Lett. 112, 063502 (2018).

    ADS  Article  Google Scholar 

  32. Dolan, G. J. Offset masks for lift-off photoprocessing. Appl. Phys. Lett. 31, 337–339 (1977).

    ADS  Article  Google Scholar 

  33. Dunsworth, A. et al. Characterization and reduction of capacitive loss induced by sub-micron Josephson junction fabrication in superconducting qubits. Appl. Phys. Lett. 111, 022601 (2017).

    ADS  Article  Google Scholar 

  34. Kurpiers, P., Walter, T., Magnard, P., Salathe, Y. & Wallraff, A. Characterizing the attenuation of coaxial and rectangular microwave-frequency waveguides at cryogenic temperatures. EPJ Quantum Technol. 4, 8 (2017).

    Article  Google Scholar 

Download references


The authors thank P.J. Duda for fabrication assistance and Y. Lu and S. Chakram for helpful discussions. The authors thank MIT Lincoln Laboratory for providing a travelling-wave parametric amplifier. This effort is supported by the Army Research Office under contract W911NF-15-2-0058. Devices and experiments were also supported by the Air Force Office of Scientific Research, and by the Department of Energy (DOE). K.J.S. was supported by NSF GRFP (NSF DGE-1144085). É.D. was supported by LDRD funds from Argonne National Laboratory. A.N.C. was supported in part by the DOE, Office of Basic Energy Sciences. D.I.S. acknowledges support from the David and Lucile Packard Foundation. This work was partially supported by the UChicago MRSEC (NSF DMR-1420709) and made use of the Pritzker Nanofabrication Facility, which receives support from SHyNE, a node of the National Science Foundation’s National Nanotechnology Coordinated Infrastructure (NSF NNCI-1542205). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government.

Author information

Authors and Affiliations



Y.P.Z. designed and fabricated the devices. Y.P.Z., H.-S.C., K.J.S., M.-H.C., J.G. and A.N.C. developed the fabrication processes. H.-S.C., K.J.S. and A.N.C. contributed to device design. Y.P.Z. performed the experiments and analysed the data. A.N.C. and D.I.S. advised on all efforts. All authors contributed to discussions and production of the manuscript.

Corresponding author

Correspondence to A. N. Cleland.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Journal peer review information: Nature Physics thanks Nicolas Sangouard and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Information.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhong, Y.P., Chang, HS., Satzinger, K.J. et al. Violating Bell’s inequality with remotely connected superconducting qubits. Nat. Phys. 15, 741–744 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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