Generation of multipartite photonic entanglement using a trapped-ion quantum processing node

TL;DR

This work demonstrates a factory-node approach for quantum networks by using a cavity-integrated trapped-ion processor to deterministically generate GHZ-type entangled photonic states, with each photon entangled to a distinct ion. The three-ion system, through a Molmer-Sorensen gate and targeted rotations, is projected into a GHZ basis, yielding eight photonic GHZ states that are verified using bespoke entanglement witnesses and polarization-parity measurements. High-fidelity ion–photon Bell states (≈0.93–0.95) and strong inter-state fidelities (≈0.97) support the reliable generation of multipartite photonic entanglement; measured three-photon GHZ fidelities (~0.76–0.78) exceed the GME threshold, with lower bounds to all eight GHZ_i± states confirming genuine multipartite entanglement. The results map established ion-entanglement techniques to traveling photons, laying a path toward distributed stored multipartite entanglement across end nodes via remote state preparation or teleportation, and outlining clear steps for scaling to larger networks and longer distances with memories and photonic-wavelength conversion.

Abstract

The ability to establish entanglement between the nodes of future quantum networks is essential for enabling a wide range of new applications in science and technology. A promising approach involves the use of a powerful central node capable of deterministically preparing arbitrary multipartite entangled states of its matter-based qubits and efficiently distributing these states to surrounding end nodes via flying photons. This central node, referred to as a ``factory node", serves as a hub for the production and distribution of multipartite entanglement. In this work, we demonstrate key functionalities of a factory node using a cavity-integrated trapped-ion quantum processor. Specifically, we program the system to generate genuinely multipartite entangled Greenberger-Horne-Zeilinger (GHZ) states of three path-switchable photons and verify them using custom-designed entanglement witnesses. These photons can, in the future, be used to establish stored multipartite entanglement between remote matter-based nodes. Our results demonstrate that the well-established techniques for the deterministic preparation of entangled states of co-trapped ion qubits can be used to prepare the same states of traveling photons, paving the way for multipartite entanglement distribution in quantum local area networks.

Figures (5)

• Figure 1: Multipartite entanglement distribution via a central factory node. (a) The factory node contains as many qubits (black circles) as there are remote nodes (here, three). Dashed lines show photonic channels, e.g., optical fibers. (b) Bell states $\ket{B}$ (blue lines) are established between factory and remote nodes via the distribution of photons Beukers_2024Duan_2010. (c)-(d) Remote state preparation: (c) Projective measurement of the factory-node qubits in a basis of multipartite entangled states $\ket{\Psi_i}\!\!\bra{\Psi_i}$ yields one of eight outcomes labelled by $i=1,\ldots,8$, resulting in the preparation of end node qubits in the state $\ket{\Psi_i}$ (orange ring); (d) Single-qubit rotations $U^i_k$ are performed at the remote nodes (labelled $k=1,2,3$), with parameters determined by the outcome in (c) to deterministically prepare any one chosen distributed state, e.g., $\ket{\Psi_1}$ (green ring).
• Figure 2: Experimental schematic. (a) Three trapped $^{40}$Ca$^{+}$ ions at neighboring anti-nodes of an 854nm vacuum standing-wave mode in an optical cavity. Raman laser pulses trigger three photons to exit the cavity in a row, each polarization-entangled with the ion that emitted it (shown by colour). Polarization analysis involves half- ($\lambda/2$) and quarter-wave ($\lambda/4$) plates, a polarising beam splitter and single-mode fiber coupled photon detectors. (b) View along the cavity axis. An acousto-optic deflector (AOD) allows switching of the 393nm photon generation (Raman) laser along the string axis. Ion fluorescence at 397nm generated during ion-qubit readout is imaged onto a digital camera. (c) Atomic energy-level diagram. $\ket{S}{=} \ket{\uparrow} = \ket{4^{2} S_{1/2,m_j{=}{-}1/2}}$, $\ket{P}{=}\ket{4^{2} P_{3/2,m_j{=}-3/2}}$, $\ket{M} =\ket{\downarrow}{=}\ket{3^{2}D_{5/2,m_j{=}-5/2}}$, $\ket{M'}{=}\ket{3^{2}D_{5/2,m_j{=}-3/2}}$.
• Figure 3: Logical polarisation probabilities and parities of three-photon GHZ states. Top panels show logical polarisation probabilities $P^{lmn}_{ijk}$ for the eight ion-qubit outcomes $lmn$ as labeled in the insets, corresponding to the eight photon states in Eqs. (\ref{['eq:ddd']}-\ref{['eq:uuu']}). Orange and blue bars show data. Red squares show simple model with height representing two standard deviations. D and A are diagonal and antidiagonal polarisations, respectively. Bottom panels show the corresponding parities $\mathcal{P}(\phi)$. Shapes show data with colours matching the bars in panels above. Solid lines: fit to the function $\mathcal{P}=C\sin{(12\phi+\alpha)}$. Dashed lines: numerical model, see Appendix \ref{['appendix:simple model']} for details.
• Figure 4: Photonic GHZ-state fidelities. Lower bounds (darker-color bars) on the fidelities $F(\rho,\ket{\mathrm{GHZ}_{i\pm}})$ to all eight GHZ states $\ket{\mathrm{GHZ}_{i\pm}}$ and exact values for $F(\rho,\ket{\mathrm{GHZ}_{1\mp}})$ (light-blue and light-red bars, respectively) are shown in the order presented in Eqs. (\ref{['eq:ddd']})–(\ref{['eq:uuu']}). Error bars show one standard deviation of the mean. The labels $\downarrow\downarrow\downarrow$, $\downarrow\downarrow\uparrow$, etc. on the bars indicate the corresponding outcomes of the ion measurements. The horizontal black line indicates the threshold of $0.5$ above which the fidelity indicates that the state $\rho$ is GME.
• Figure A.1: Histograms of photon-arrival times. Data are taken from the results of measurements in the eight bases presented in Table \ref{['settings']}. Probability densities are shown on the vertical axis: The number of counts has been normalized by the number of attempts and by the 1µs time-bin width. Three single-photon wave packets are visible: The color denotes the ion that is expected to have produced the photon (c.f. Fig. \ref{['fig:experimental_schematic']}). Black dashed vertical lines indicate the three 50µs-long time windows in which data is subsequently analysed.