Direct generation of three-photon polarization entanglement

Journal name:
Nature Photonics
Year published:
Published online


Non-classical states of light are of fundamental importance for emerging quantum technologies. All optics experiments producing multi-qubit entangled states have until now relied on outcome post-selection, a procedure where only the measurement results corresponding to the desired state are considered. This method severely limits the usefulness of the resulting entangled states. Here, we show the direct production of polarization-entangled photon triplets by cascading two entangled downconversion processes. Detecting the triplets with high-efficiency superconducting nanowire single-photon detectors allows us to fully characterize them through quantum state tomography. We use our three-photon entangled state to demonstrate the ability to herald Bell states, a task that was not possible with previous three-photon states, and test local realism by violating the Mermin and Svetlichny inequalities. These results represent a significant breakthrough for entangled multi-photon state production by eliminating the constraints of outcome post-selection, providing a novel resource for optical quantum information processing.

At a glance


  1. Polarization entangled photons using cascaded spontaneous parametric downconversion.
    Figure 1: Polarization entangled photons using cascaded spontaneous parametric downconversion.

    a, Schematic of the source. The first entangled photon source (EPS 1) produces entangled photons in modes 0 and 1. The photon in mode 0 is used to pump the second entangled photon source (EPS2), thus transferring the entanglement to two new photons in modes 2 and 3 to produce a GHZ state. b, Detailed set-up of the experiment. A Sagnac source produces entangled photon pairs at 842 nm and 776 nm using a periodically poled potassium titanyl phosphate (PPKTP) crystal. The photons at 776 nm are used to pump a Mach–Zehnder source, which produces entangled photons at 1,530 nm and 1,570 nm in periodically poled lithium niobate (PPLN) waveguides. The three-photon state is analysed using controllable measurement settings implemented with motorized wave plates (A1, A2 and A3) and polarizing beamsplitters. Photons at 842 nm are detected using silicon avalanche photodiodes (APDs), while photons at telecom wavelengths are detected using SNSPDs. The signal from all detectors is sent to a time-tagging unit. The phase in the interferometer is controlled using a piezo-controller and a proportional-integral-derivative (PID) controller. See Methods for additional details.

  2. Measurement to determine optimal phase.
    Figure 2: Measurement to determine optimal phase.

    a,b, Measured triplets with positive (black squares) and negative (red circles) contributions to the diagonal basis correlation (a) and the corresponding correlation E(σx,σx,σx) (b). The line is a sinusoidal fit with the amplitude and phase as fitting parameters, from which we extract an amplitude of 0.82 ± 0.03. Setting the quarter-wave plate (QWP) tilt angle ϑ to 11° produces a relative phase of (0.44 ± 0.03)π and minimizes the correlation, resulting in a |GHZ〉 state. The error bars represent one standard deviation calculated from Poissonian counting statistics.

  3. Two-dimensional histogram of time differences between detected photon events.
    Figure 3: Two-dimensional histogram of time differences between detected photon events.

    The large peak corresponds to photon triplets from cascaded downconversion, showing that they have tight time correlations. The line above the background at t3 − t2 ≈ 7 ns is the main source of accidental triplets. This is due to events where a photon pair produced in the second downconversion is detected within 15 ns of an unrelated photon at 842 nm. The reason a similar line is not seen for a constant value of t2 − t1 is that the count rates at detectors 2 and 3 are three orders of magnitude smaller than those at D1, so an accidental threefold coincidence is much more likely to involve an uncorrelated photon at D1. The resulting signal-to-noise ratio in this histogram is 73:1.

  4. Reconstructed three-photon density matrix.
    Figure 4: Reconstructed three-photon density matrix.

    a,b, Real (a) and imaginary (b) parts of the density matrix, which is reconstructed from the measured threefold coincidences with no background subtraction.

  5. Real and imaginary parts of the reconstructed density matrices of the heralded two-photon states.
    Figure 5: Real and imaginary parts of the reconstructed density matrices of the heralded two-photon states.

    The density matrices are reconstructed from 1,632 triplets, which were measured in 3.6 h. a,b, Heralding with |D〉 results in a state close to |Φ+〉. c,d, Heralding with |A〉 results in a state close to |Φ〉. e,f, When heralding with |D〉 and |A〉 but ignoring the measurement outcomes, the coherent terms vanish, resulting in an incoherent mixture of |HH〉 and |VV〉.


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Author information


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

    • Deny R. Hamel,
    • Lynden K. Shalm,
    • Kevin J. Resch &
    • Thomas Jennewein
  2. Département de physique et d'astronomie, Université de Moncton, Moncton, New Brunswick E1A 3E9, Canada

    • Deny R. Hamel
  3. National Institute of Standards and Technology, 325 Broadway, MC 815.04, Boulder, Colorado 80305, USA

    • Lynden K. Shalm,
    • Aaron J. Miller,
    • Francesco Marsili,
    • Varun B. Verma,
    • Richard P. Mirin &
    • Sae Woo Nam
  4. Department of Physics, Stockholm University, S-10691 Stockholm, Sweden

    • Hannes Hübel
  5. Department of Physics, Albion College, Albion, Michigan 49224, USA

    • Aaron J. Miller


D.R.H., L.K.S., H.H., K.J.R. and T.J. planned the experiment. D.R.H., L.K.S. and H.H. built the experimental set-up. D.R.H. carried out the experiment and analysed the data. A.J.M., F.M., V.B.V., R.P.M. and S.W.N. developed the detector system. All authors contributed to the writing of the manuscript.

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