Multi-photon entanglement in high dimensions

Journal name:
Nature Photonics
Year published:
Published online

Forming the backbone of quantum technologies today, entanglement1, 2 has been demonstrated in physical systems as diverse as photons3, ions4 and superconducting circuits5. Although steadily pushing the boundary of the number of particles entangled, these experiments have remained in a two-dimensional space for each particle. Here we show the experimental generation of the first multi-photon entangled state where both the number of particles and dimensions are greater than two. Two photons in our state reside in a three-dimensional space, whereas the third lives in two dimensions. This asymmetric entanglement structure6 only appears in multiparticle entangled states with d > 26. Our method relies on combining two pairs of photons, high-dimensionally entangled in their orbital angular momentum7. In addition, we show how this state enables a new type of ‘layered’ quantum communication protocol. Entangled states such as these serve as a manifestation of the complex dance of correlations that can exist within quantum mechanics.

At a glance


  1. Schematic of the experiment.
    Figure 1: Schematic of the experiment.

    A blue laser pulse creates two pairs of OAM-entangled photons in two nonlinear crystals (NL1 and NL2). Both pairs are spatially separated via polarising beam splitters (PBS). A moving trombone prism ensures that a photon from each pair arrives simultaneously at the OAM beam splitter. This device contains two dove-prisms (DP1 and DP2). DP1 reflects an incoming photon that inverts its spiral phase front, whereas DP2 both inverts and rotates it by 180°. This results in interference that depends on the parity (odd or even) of the spatial mode. Considered as a whole, the OAM beam splitter reflects odd components of OAM and transmits even ones, mixing the OAM components of two input photons. Depicted for clarity as a Mach–Zehnder interferometer, this was implemented in a modified Sagnac configuration for increased stability (see Supplementary Fig. 1 for an in-depth schematic). A coincidence between detectors B and C can only arise when both detected photons have the same mode parity. This projects photons at detectors (A–C) into an asymmetric three-photon entangled state that is entangled in 3 × 3 × 2 dimensions of its OAM. The detection of a trigger photon at detector T heralds the presence of this state.

  2. Three-photon coherent superposition.
    Figure 2: Three-photon coherent superposition.

    Experimental data showing the result of measuring photons A–C in superposition states , and , respectively, conditioned on measuring photon D in state . The drop in coincidence counts at the position of zero delay results from interference between photons B and C. This indicates that the three-photon state from equation (4) is in a coherent superposition. A Gaussian fit is calculated based on the spectral shape of our narrowband filters and has a full-width at half-maximum of 473 μm and a visibility of 63.5% (see Methods for details). Error bars indicate the Poissonian error in the photon-counting rate.

  3. Witnessing genuine multipartite entanglement in high dimensions.
    Figure 3: Witnessing genuine multipartite entanglement in high dimensions.

    a, To verify that our three-photon state is entangled in 3 × 3 × 2 dimensions, we have to show that it cannot be decomposed into entangled states of a smaller dimensionality structure. First, we calculate the best achievable overlap of a (3,2,2) state σ with an ideal target (3,3,2) state |Ψ〉 to be Fmax = 2/3. Next, we calculate the overlap Fexp of our experimentally generated state ρexp with the target state |Ψ〉. b, The 18 diagonal and 3 unique off-diagonal elements of ρexp that are measured to calculate a value of Fexp = 0.801 ± 0.018 (elements not measured are filled in with crossed lines). This is above the bound of Fmax = 0.667 by 7 standard deviations and verifies that the generated state is genuinely multipartite entanglement in 3 × 3 × 2 dimensions of its OAM. Fexp does not reach its maximal value of 1 because the state superposition is not perfectly coherent. Theoretical values are shown by empty bars.

  4. A layered quantum communication protocol.
    Figure 4: A layered quantum communication protocol.

    a, When Alice, Bob, and Carol share an asymmetric (3,3,2) entangled state, all three have access to an entangled bit in the (0,1) basis. Moreover, whenever Carol has a 1, Alice and Bob share an entangled bit on the (1,2) basis. b, After sufficient data is collected, these bits can be used as a one-time pad to encrypt a secret message shared among all three parties. In addition, Alice and Bob can share a second layer of information unknown to Carol. Security is verified by checking for the presence of (3,3,2) entanglement in a randomly selected subset of photons.


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Author information

  1. Present address: Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, Ottawa K1N 6N5, Canada

    • Robert Fickler


  1. Austrian Academy of Sciences, Institute for Quantum Optics and Quantum Information (IQOQI), Boltzmanngasse 3, A-1090 Vienna, Austria

    • Mehul Malik,
    • Manuel Erhard,
    • Mario Krenn,
    • Robert Fickler &
    • Anton Zeilinger
  2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria

    • Mehul Malik,
    • Manuel Erhard,
    • Mario Krenn,
    • Robert Fickler &
    • Anton Zeilinger
  3. Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

    • Marcus Huber
  4. ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona, Spain

    • Marcus Huber
  5. Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland

    • Marcus Huber


M.M. devised the concept of the experiment, with assistance from M.K. and R.F. M.M and M.E. performed the experiment. M.H. developed the high-dimensional entanglement witness. M.M., M.E., M.K. and M.H. analysed the data. M.M. and M.H. developed the layered quantum communication protocol. A.Z. initiated the research and supervised the project. M.M. wrote the manuscript with contributions from all authors.

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The authors declare no competing financial interests.

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