Experimental three-photon quantum nonlocality under strict locality conditions

Journal name:
Nature Photonics
Year published:
Published online


Quantum correlations, often observed as violations of Bell inequalities1, 2, 3, 4, 5, are critical to our understanding of the quantum world, with far-reaching technological6, 7, 8, 9 and fundamental impact. Many tests of Bell inequalities have studied pairs of correlated particles. However, interest in multi-particle quantum correlations is driving the experimental frontier to test larger systems. All violations to date require supplementary assumptions that open results to loopholes, the closing of which is one of the most important challenges in quantum science. Seminal experiments have closed some loopholes10, 11, 12, 13, 14, 15, 16, but no experiment has closed locality loopholes with three or more particles. Here, we close both the locality and freedom-of-choice loopholes by distributing three-photon Greenberger–Horne–Zeilinger entangled states17 to independent observers. We measured a violation of Mermin's inequality18 with parameter 2.77 ± 0.08, violating its classical bound by nine standard deviations. These results are a milestone in multi-party quantum communication19 and a significant advancement of the foundations of quantum mechanics20.

At a glance


  1. Experimental set-up.
    Figure 1: Experimental set-up.

    The downconversion (SPDC) source of triggered three-photon GHZ states and Alice were located in the RAC building. Two of the entangled photons were sent to the roof through optical fibres and transmitted to trailers Bob and Charlie through free-space optical links. Bob and Charlie were 801 m and 721 m away from the source, respectively, and the optical links used to send their photons were 772 m and 686 m long, respectively. Bob and Charlie measured their photon polarizations in one of two bases, determined by co-located QRNGs and fast Pockels cells (PCs), and recorded measurement values using time-tagging electronics. A third trailer, Randy, 446 m from the source, contained a QRNG that sent random bits to Alice over a 425 m RF link determining the setting of Alice's PC. Randy contained time-tagging electronics to record the output of the QRNG for comparison with Alice's record. Alice's photon was delayed in a fibre spool before its polarization was measured and the result recorded using time-tagging electronics. HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarizing beamsplitter; APD, avalanche photodiode; SMF, single-mode fibre.

  2. Experimentally measured three-photon polarization correlations.
    Figure 2: Experimentally measured three-photon polarization correlations.

    The analysers were set to the R/L basis for settings a, b and c and the D/A basis for settings a′, b′ and c′. During a 1 h 19 min experiment, we measured 2,472 fourfold coincidence events, of which 1,232 were used to extract correlations for a test of Mermin's inequality. The measured correlations were E(a,b,c= 0.689 ± 0.040, E(a,b′,c′) = −0.710 ± 0.042, E(a′,b,c′) = −0.718 ± 0.038 and E(a′,b′,c= −0.655 ± 0.044, yielding a Mermin parameter of 2.77 ± 0.08, which violates the local hidden-variable bound of 2 by over 9σ. Error bars represent one standard deviation based on Poisson statistics.

  3. Space-time analysis of the experiment.
    Figure 3: Space–time analysis of the experiment.

    a, Simplified layout of the experiment showing the straight-line distances and angles between locations. be Six two-dimensional space–time diagrams fully describe the relationship between important events in the experiment in the laboratory frame, namely, the entangled photon creation event labelled ‘State creation’, choices of measurement bases and the measurements themselves. Insets: relevant locations for each panel. The earliest and latest times at which Bob's measurement basis could have been selected are labelled ‘Bob basis early’ and ‘Bob basis late’, respectively. Labelling at Randy and Charlie follows this convention. The event corresponding to the measurement of a photon from the source at Bob is labelled ‘Bob measurement’, and similarly for Alice and Charlie. The light cones for the important events are shown as diagonal lines and shaded regions for Source/Alice (red), Bob (green), Charlie (blue) and Randy (orange). Red vertical arrows indicate tolerances for the freedom-of-choice (FoC) and locality (L) conditions. The minimum tolerance for the FoC is 304 ± 25 ns, as seen in b, and the minimum for the locality condition is 264 ± 28 ns, as seen in d, indicating that both conditions are met by a significant margin.


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Author information


  1. Institute for Quantum Computing and Department of Physics & Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

    • C. Erven,
    • E. Meyer-Scott,
    • K. Fisher,
    • J. Lavoie,
    • B. L. Higgins,
    • Z. Yan,
    • C. J. Pugh,
    • J.-P. Bourgoin,
    • R. Prevedel,
    • L. K. Shalm,
    • L. Richards,
    • N. Gigov,
    • R. Laflamme,
    • G. Weihs,
    • T. Jennewein &
    • K. J. Resch
  2. Centre for Quantum Photonics, H.H. Wills Physics Laboratory & Department of Electrical and Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK

    • C. Erven
  3. Centre for Ultrahigh Bandwidth Devices for Optical Systems (CUDOS) & MQ Photonics Research Centre, Department of Physics & Astronomy, Macquarie University, Sydney, New South Wales 2109, Australia

    • Z. Yan
  4. Research Institute of Molecular Pathology and Max F. Perutz Laboratories GmbH, Dr Bohr-Gasse 7–9, 1030, Vienna, Austria

    • R. Prevedel
  5. National Institute of Standards and Technology, 325 Broadway Street, Boulder, Colorado 80305, USA

    • L. K. Shalm
  6. Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria

    • G. Weihs


C.E., R.L., G.W., T.J. and K.J.R. conceived the experiment. C.E., E.M.S., K.F., J.L., B.L.H., Z.Y., C.P., J.P.B., R.P., L.R. and N.G. constructed the experiment. B.L.H. and L.K.S. performed the space–time analysis. C.E., E.M.S., K.F., J.L., C.P. and J.P.B. collected the data. C.E. analysed the data. All authors contributed to writing the manuscript.

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