Generation of hybrid entanglement of light

Journal name:
Nature Photonics
Year published:
Published online


Entanglement between quantum and classical objects is of special interest in the context of fundamental studies of quantum mechanics and potential applications for quantum information processing. In quantum optics, single photons are treated as light quanta while coherent states are considered the most classical of pure states. Recently, entanglement between a single photon and a coherent state in a free-travelling field was identified as a useful resource for optical quantum information processing. However, the extreme difficulty involved in generating such states was highlighted, as it requires clean cross-Kerr nonlinearities. Here, we devise and experimentally demonstrate a scheme to generate such hybrid entanglement by implementing a superposition of two distinct quantum operations. The generated states clearly show entanglement between the two different types of states. Our work opens the way to the generation of hybrid entanglement of greater size and the development of efficient quantum information processing using a new type of qubit.

At a glance


  1. Scheme for generating hybrid entanglement of light.
    Figure 1: Scheme for generating hybrid entanglement of light.

    a, Conceptual schematic for generating small-scale hybrid entanglement by superposing two photon-addition operations on different spatial modes. The phase-space displacement operation on mode 2 is then obtained by mixing with an additional intense coherent field (|βright fence) on a low-reflectivity beamsplitter. D1 and D2 are two single-photon detectors. b, Contour plot for fidelity between the ideal hybrid entangled state and the model state |ΨS right fence that can be generated by the proposed scheme as a function of the initial amplitude αi and the final amplitude αf. The solid curve corresponds to the fidelities maximized over αf for given values of αi and the dashed curve to fidelities maximized over αi for given values of αf.

  2. Experimental generation of hybrid entanglement of light using temporal modes.
    Figure 2: Experimental generation of hybrid entanglement of light using temporal modes.

    a, Temporal-mode version of the proposed scheme, as used in the experiment. Here, an unbalanced Mach–Zehnder interferometer makes the ‘clicks’ heralding photon addition onto the two temporal modes (1 and 2) indistinguishable. This results in a superposition of photon-addition operations on the two modes containing vacuum (|0right fence) and a coherent state (|αright fence), respectively. The state displacement is again obtained by mixing with an additional intense coherent state (|βright fence), only synchronized with the second temporal mode. b, Actual experimental scheme. Tp, delay between successive pulses from the mode-locked laser; PC, fibre polarization controller; R/T, variable-ratio fibre beamsplitter; D1, fibre-coupled avalanche photodiode (APD); HWP1 and HWP2, half-wave plates; PBS, polarizing beamsplitter used for the displacement operation. The locking mechanism of the fibre Mach–Zehnder interferometer is not shown, for clarity. (See text and Methods for further details.).

  3. Experimental hybrid entanglement.
    Figure 3: Experimental hybrid entanglement.

    a, Reconstructed density matrix for the experimentally generated hybrid entangled state of equation (6) with αi    1.4. In this case we use 3 × 3 blocks of 10 × 10 matrix elements, and we correct for a detection efficiency of 61%. The two insets show the Wigner functions for the state in the second mode when vacuum or a single photon are observed in the first. b, Plot of NPT as a function of the initial coherent state amplitude αi. The solid curve indicates the calculated NPT for model state |ΨOright fence. Data points represent the NPT derived from experimentally reconstructed density matrices, corrected for detection efficiency. Error bars of statistical origin (related to the number of homodyne data acquisitions) are of the order of 2% and within the size of the plotted data points.

  4. Experimental symmetric hybrid entanglement.
    Figure 4: Experimental symmetric hybrid entanglement.

    a, Experimentally reconstructed density matrix for a symmetric, small-scale, hybrid entangled state, as obtained after phase-space coherent displacement. Correction for the detection efficiency of 63% has been made in the reconstruction. Because of the small effective amplitude (αf    0.31), the number of reconstructed elements in the Fock space has been decreased correspondingly. b, Calculated density matrix for the model |ΨS right fence state. c, Calculated density matrix for the ideal hybrid state |Ψ(αf  =  0.31)right fence.


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Author information


  1. Center for Macroscopic Quantum Control, Department of Physics and Astronomy, Seoul National University, Seoul, 151-742, Korea

    • Hyunseok Jeong,
    • Minsu Kang &
    • Seung-Woo Lee
  2. Istituto Nazionale di Ottica (INO-CNR), Largo Enrico Fermi 6, 50125 Florence, Italy

    • Alessandro Zavatta,
    • Luca S. Costanzo,
    • Samuele Grandi &
    • Marco Bellini
  3. LENS and Department of Physics, University of Firenze, 50019 Sesto Fiorentino, Florence, Italy

    • Alessandro Zavatta,
    • Luca S. Costanzo &
    • Marco Bellini
  4. Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, Queensland 4072, Australia

    • Timothy C. Ralph
  5. Present address: Centre for Cold Matter, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK

    • Samuele Grandi


H.J. and T.C.R. proposed the experiment and developed the theoretical models. M.K. and S.-W.L. performed theoretical analysis and numerical simulations. L.S.C. and S.G. ran the experiment and data analysis. A.Z. and M.B. proposed, planned and coordinated the experiment and data analysis. All authors discussed the results and implications of the experiment and contributed to writing the manuscript.

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The authors declare no competing financial interests.

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