A building block of quantum repeaters for scalable quantum networks

Abstract

Quantum networks, integrating quantum communication, quantum metrology, and distributed quantum computing, could provide secure and efficient information transfer, high-resolution sensing, and an exponential speed-up in information processing. Deterministic entanglement distribution over long distances is a prerequisite for scalable quantum networks, enabling the utilization of device-independent quantum key distribution (DI-QKD) and quantum teleportation to achieve secure and efficient information transfer. However, the exponential photon loss in optical fibres prohibits efficient and deterministic entanglement distribution. Quantum repeaters, incorporating entanglement swapping and entanglement purification with quantum memories, offer the most promising means to overcome this limitation in fibre-based quantum networks. Despite numerous pioneering efforts toward realizing quantum repeaters, a critical bottleneck remains, as remote memory-memory entanglement suffers from decoherence more rapidly than it can be established and purified over long distances. We overcome this by developing long-lived trapped-ion memories, an efficient telecom interface, and a high-visibility single-photon entanglement protocol. This allows us to establish and maintain memory-memory entanglement over a 10 km fibre within the average entanglement establishment time for the same distance. As a direct application, we demonstrate metropolitan-scale DI-QKD, distilling 1,917 secret keys out of 4.05*10^5 Bell pairs over 10 km. We further report a positive key rate over 101 km in the asymptotic limit, extending the achievable distance by more than two orders of magnitude. Our work provides a critical building block for quantum repeaters and marks an important step toward scalable quantum networks.

Figures (4)

• Figure 1: Experimental setup schematics: (a) Overview of Experimental setup. Single photons generated from two independent trapped-ion nodes interfere at a midpoint along the fibre spool. Successful photon detection on either detectors at the middle station heralds ion–ion entanglement. (b) Laser beams at 729 and 854 nm for coherent state manipulation and single photon generation are sent into the trap along the optic axis of objectives. The same beams also generate 393 nm phase reference pulse via sum-frequency generation before the trap. (c) The 393 nm photons are combined with a 527 nm pump laser beam at a dichroic mirror and converted to 1550 nm via waveguide-based difference-frequency generation. A 1548 nm phase reference beam is coupled into the optical link via a dense wavelength-division multiplexer (DWDM) to pre-stabilize the long fibre.
• Figure 2: Entanglement generation: (a) Energy level diagram of a calcium-40 ion, illustrating single-photon generation via the metastable $\left| \uparrow \right\rangle$ and the excited states $\left| e \right\rangle$, and single qubit rotation between two Zeeman sub-levels $\left| \downarrow \right\rangle$ and $\left| e \right\rangle$ using Raman transitions. (b) Temporal profile of single photons at 393 and 1550 nm, detected using a PMT and a SNSPD respectively. (c) Efficiency and noise characteristics of the QFC module (393 nm$\rightarrow$1550 nm) as a function of pump power at 527 nm after transmission through a 10 km fibre link. (d) Contrast measurement for the phase reference laser, with the corresponding standard deviation shown. The inset shows the histogram of detector counts at the point of maximum contrast.
• Figure 3: Entanglement fidelity: (a) Quantum state tomography and $\braket{XX}$-parity analysis at a fibre length of 10 km, with error bars indicating the standard deviation. $\mathrm{X}$, $\mathrm{Y}$, and $\mathrm{Z}$ denote the Pauli operators $\sigma_x$, $\sigma_y$, and $\sigma_z$, respectively. (b) Fidelity of the $\rho_{\pm}$ states, with error bars indicating the standard deviation, extracted from the population and parity measurement as a function of the excitation parameter $\alpha$ and entanglement generation rate. (c) Infidelity as a function of fibre length, with error bars denoting the standard deviation. Contributions are attributed to protocol-induced error (1), ion-related effects (2, 5), and photon-related factors (3, 4), following the numbering defined in the main text. (d) The entanglement fidelities (orange squares) are shown for different storage times, while the corresponding expectation values of $\braket{XX}$ (red circles) and $\braket{ZZ}$ (green diamonds) are shown in the inset. The error bars representing one standard deviation. The probability distribution of intervals between two consecutive entanglement events is plotted with a bin size of 10 ms.
• Figure 4: DI-QKD results: (a) Alice and Bob are connected via a quantum network link. Each party receives inputs $\mathrm{X}$ and $\mathrm{Y}$ and generates outputs $\mathrm{a}$ and $\mathrm{b}$, respectively. The results are stored locally and communicated via an authenticated public classical channel for post-processing. (b) Blue curve: data accumulation over time; red regions: pauses for system recovery. (c) Accumulated CHSH (blue) and QBER (orange) values, with one-standard-deviation uncertainties shown as shaded regions. Inset: finite-key DI-QKD over a 10-km fibre link with total failure probability $\epsilon = 10^{-5}$. (d) Infinite-key analysis of DI-QKD over a 101-km fibre. Results are shown in the limit where the fraction of key-generation rounds approaches unity, with error bars representing one standard deviation for the CHSH value and QBER, compared with Ref.zhang2022device.