Requirements for Teleportation in an Intercity Quantum Network

TL;DR

The paper develops an analytic, hardware-aware framework to determine minimal improvements needed to achieve end-to-end quantum teleportation fidelity above the classical limit $2/3$ in an intercity network consisting of two metropolitan networks linked by a backbone. By modeling entanglement generation, memory decoherence, and cut-off strategies with Werner-state noise, it derives closed-form expressions for teleportation rate and fidelity and validates them against NetSquid simulations. An optimization scheme, grounded in a cost function over baseline and optimistic parameter values, identifies minimal per-parameter improvements and highlights the metropolitan link generation probability as a key lever. Case studies with trapped-ion MNs and ensemble-memory backbone show metropolitan teleportation is feasible with current state-of-the-art hardware for ER, while QR and intercity teleportation require near-term hardware advances, particularly in backbone performance. The framework offers practical design guidance for heterogeneous quantum networks and can be extended to longer repeater chains and VBQC/QKD-focused scenarios.

Abstract

We investigate the hardware requirements for quantum teleportation in an intercity-scale network topology consisting of two metropolitan-scale networks connected via a long-distance backbone link. Specifically, we identify the minimal improvements required beyond the state-of-the-art to achieve an end-to-end expected teleportation fidelity of $2/3$, which represents the classical limit. To this end, we formulate the hardware requirements computation as optimisation problems, where the hardware parameters representing the underlying device capabilities serve as decision variables. Assuming a simplified noise model, we derive closed-form analytical expressions for the teleportation fidelity and rate when the network is realised using heterogeneous quantum hardware, including a quantum repeater chain with a memory cut-off. Our derivations are based on events defined by the order statistics of link generation durations in both the metropolitan networks and the backbone, and the resulting expressions are validated through simulations on the NetSquid platform. The analytical expressions facilitate efficient exploration of the optimisation parameter space without resorting to computationally intensive simulations. We then apply this framework to a representative realisation in which the metropolitan nodes are based on trapped-ion processors and the backbone is composed of ensemble-based quantum memories. Our results suggest that teleportation across metropolitan distances is already achievable with state-of-the-art hardware when the data qubit is prepared after end-to-end entanglement has already been established, whereas extending teleportation to intercity scales requires additional, though plausibly achievable, improvements in hardware performance.

Figures (8)

• Figure 1: Schematic of an intercity quantum network architecture comprising four different components. User-controlled end nodes are denoted by circles $\text{P}_1$--$\text{P}_4$ and metropolitan hubs by squares $\text{H}_1$--$\text{H}_2$. The border nodes, shown as diamonds $\text{B}_1$--$\text{B}_2$, form the backbone together with the zig-zag line, which can be realised using either a space-based quantum communication channel or a terrestrial linear quantum repeater chain, with individual repeater nodes depicted as triangles. Each end node is connected to its nearest hub $25\,$km away and forms a metropolitan network (MN $1$ or $2$). The $450\,$km backbone connects the metropolitan regions via the border nodes at both ends. Together, the MNs and the backbone form the full IN, enabling long-distance quantum communication between multiple end nodes.
• Figure 3: Comparison of analytical (lines) and simulation results (dots) for qubit-ready teleportation in an MN. The mean, along with the 5th and 95th percentiles of the performance metrics, is shown as a function of the base efficiency $p_\text{m}^0$. (a) The expected teleportation fidelity is evaluated for both baseline and optimistic values of memory coherence time $t_\text{coh}$ and metropolitan link fidelity $f_{\text{m}'}$, while (b) the teleportation rate depends solely on $p_\text{m}^0$. Simulation results closely match the analytical values.
• Figure 4: Requirements to achieve the target teleportation fidelity of $2/3$ in an MN. The surfaces represent the minimum required metro link fidelity $f_{\text{m}'}$ as a function of $p_\text{m}^0$ and $t_\text{coh}$ for (a) entanglement-ready and (b) qubit-ready teleportation. The colour of the surface shows the corresponding teleportation rate. The baseline (denoted B) in (a) already achieves the target fidelity of teleportation, while an optimal (denoted O) parameter configuration subject to hardware cost $c$ is shown in (b). The $(p_\text{m}^0, t_\text{coh}, f_{\text{m}'})$ coordinates of the points in (b) are B: ${(5.95\times 10^{-4}, 62\,\text{ms}, 0.88)}$ and O: ${(1.43\times 10^{-2}, 196\,\text{ms}, 0.88)}$.
• Figure 5: Comparison of analytical (lines) and simulation results (dots) for the expected teleportation fidelity as a function of cut-off time $t_\text{cut}$ for (a) entanglement-ready and (b) qubit-ready teleportation. Each simulation point corresponds to the mean fidelity of batch average values, with error bars denoting the $5$th and $95$th percentiles across batch averages. The entanglement generation probabilities $p_\text{m}^0$, and $p_\text{b}$ are set at their baseline ($\underline{p}_\text{m}^0\!=\! 5.95\times 10^{-4}$, $\underline{p}_\text{b}\!=\!1.51\times 10^{-6}$) and optimistic values ($\overline{p}_\text{m}^0\!=\!1.43\times 10^{-2}$, $\overline{p}_\text{b}\!=\!4.18\times 10^{-3}$), as indicated in the legend. All remaining parameters are fixed at their respective optimistic values, i.e., $\overline{f}_\text{m}\!=\!0.95$, $\overline{t}_\text{coh}\!=\!4\,\text{s}$, and $\overline{f}_\text{b}\!=\!0.90$. The analytical expected teleportation fidelity matches closely with the empirical mean.
• Figure 6: Comparison of analytical (lines) and simulation results (dots) for the teleportation rate as a function of cut-off time $t_\text{cut}$. Each simulation point represents the mean of rates computed across batches, and error bars indicate the $5$th and $95$th percentiles of batch averages. The entanglement generation probabilities $p_\text{m}^0$, and $p_\text{b}$ are set at their baseline ($\underline{p}_\text{m}^0\!=\! 5.95\times 10^{-4}$, $\underline{p}_\text{b}\!=\!1.51\times 10^{-6}$) and optimistic values ($\overline{p}_\text{m}^0\!=\!1.43\times 10^{-2}$, $\overline{p}_\text{b}\!=\!4.18\times 10^{-3}$), as indicated in the legend. The coherence time $t_\text{coh}$ is fixed at its optimistic value $4\,\text{s}$. The strong agreement between simulation results and analytical predictions confirms the validity of the analytical model.

Theorems & Definitions (10)

• Theorem 1
• proof
• Lemma 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Lemma 2
• proof