Remote creation of hybrid entanglement between particle-like and wave-like optical qubits

Journal name:
Nature Photonics
Year published:
Published online


The wave–particle duality of light has led to two different encodings for optical quantum information processing. Several approaches have emerged based either on particle-like discrete-variable states (that is, finite-dimensional quantum systems) or on wave-like continuous-variable states (that is, infinite-dimensional systems). Here, we demonstrate the generation of entanglement between optical qubits of these different types, located at distant places and connected by a lossy channel. Such hybrid entanglement, which is a key resource for a variety of recently proposed schemes, including quantum cryptography and computing, enables information to be converted from one Hilbert space to the other via teleportation and therefore the connection of remote quantum processors based upon different encodings. Beyond its fundamental significance for the exploration of entanglement and its possible instantiations, our optical circuit holds promise for implementations of heterogeneous network, where discrete- and continuous-variable operations and techniques can be efficiently combined.

At a glance


  1. Measurement-induced hybrid entanglement.
    Figure 1: Measurement-induced hybrid entanglement.

    a, Distant nodes of a quantum network can rely on different information encodings, that is, continuous or discrete variables. A router enables hybrid entanglement to be established between the nodes at a distance. For instance, Alice sends one mode of a weak two-mode squeezed state |0right fence|0right fence + λ|1right fence|1right fence towards the router, while Bob transmits a small part of a cat state |αright fence + |αright fence. The two modes interfere in an indistinguishable fashion on a beamsplitter. Each detection event at the output heralds the generation of hybrid entanglement between Alice and Bob, which can be used for further processing or teleportation. b, Experimental set-up. Alice and Bob locally generate the required resources by using continuous-wave OPOs operated below threshold. A two-mode squeezer and a single-mode squeezer are used, respectively, on Alice's node and Bob's node. A small fraction of Bob's squeezed vacuum, which is a good approximation of an even cat state for |α|   1, is tapped (3%) and mixed at a central station with the idler beam generated by Alice. The resulting beam is then frequency filtered (conditioning path) and detected by a superconducting single-photon detector (SSPD). Given a detection event, which heralds entanglement generation, the hybrid entangled state is characterized by two high-efficiency homodyne detections. Photodiodes P1, P2 and P3 are used for phase control and stabilization. The beamsplitter ratio in the central station enables the relative weights in the superposition to be chosen. FP, Fabry–Pérot cavity; IF, interferential filter; PBS, polarizing beamsplitter; LO, local oscillator.

  2. Experimental quantum state tomography.
    Figure 2: Experimental quantum state tomography.

    The relative phase is set to ϕ = π and the beamsplitter ratio in the central station is adjusted to generate a maximally entangled state, that is, with equal weights. a, Wigner functions associated with the reduced density matrices with k,l  {0,1,2}, without and with correction for detection losses (η = 85%). The components with k ≠ l not being Hermitian, the corresponding Wigner functions are not necessarily real, but conjugate. The plot therefore gives the real part in the back corner (k > l) and the imaginary part in the front corner (k > 1). b, Wigner functions associated with the reduced density matrices with k,l  {+ , −}, corrected for detection losses. |+right fence and |right fence stand, respectively, for the rotated basis and . The higher-photon-number terms are no longer represented as they are negligible, as shown in a. Corrected for detection losses, the fidelity is 77 ± 3% with the targeted state with ϕ = π and |α| = 0.9.

  3. Experimental quantum states from separable to maximally entangled.
    Figure 3: Experimental quantum states from separable to maximally entangled.

    The relative phase is set to ϕ = 0 and the beamsplitter ratio at the central station is tuned. The blocks provide the Wigner functions associated with the reduced density matrices with k,l  {0,1}. The higher-photon-number terms are not represented as they are negligible. For each generated state, the negativity (equal to 0.5 in the ideal case) is computed from the full two-mode density matrix, showing the transition from separable to maximally entangled state and back to separable.


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Author information


  1. Laboratoire Kastler Brossel, Université Pierre et Marie Curie, Ecole Normale Supérieure, CNRS, 4 place Jussieu, 75252 Paris Cedex 05, France

    • Olivier Morin,
    • Kun Huang,
    • Jianli Liu,
    • Hanna Le Jeannic,
    • Claude Fabre &
    • Julien Laurat
  2. State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China

    • Kun Huang


J.L. and O.M. conceived the experiment. O.M., K.H., J.Liu and H.L.J. carried out the experiment and analysed the data, under the supervision of J.L. O.M, K.H., H.L.J., C.F. and J.L. contributed to discussing the implementation and the results. O.M., K.H. and J.L. wrote the manuscript.

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