Requirements for Teleportation in an Intercity Quantum Network

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.

💡 Research Summary

The paper addresses the concrete hardware requirements needed to achieve quantum teleportation across an intercity‑scale quantum network (IN) that consists of two metropolitan‑scale networks (MNs) linked by a long‑distance backbone. The authors aim to determine the minimal improvements beyond current state‑of‑the‑art technology required to reach an expected teleportation fidelity of 2/3, the classical limit, thereby demonstrating a genuine quantum advantage.

The network model is described in detail: each MN contains end‑user nodes (P1‑P4) connected to local hubs (H1‑H2) by 25 km fibers, while the backbone connects the two hubs over 450 km via a chain of quantum repeaters (B1‑B2). The repeaters are equipped with quantum memories, and the whole system is assumed to operate under standard conditions: heralded entanglement generation (HEG), depolarising memory noise, instantaneous local gates, a “swap‑as‑soon‑possible” (swap‑ASAP) policy, a memory cut‑off strategy, and deterministic teleportation (unit success probability).

Two operational regimes are considered. In the Entanglement‑Ready (ER) scenario, the data qubit to be teleported is prepared only after an end‑to‑end entangled link has been successfully established, thus avoiding decoherence of the data qubit during the probabilistic entanglement generation phase. In the Qubit‑Ready (QR) scenario, the data qubit is prepared in advance and stored in memory until the entangled link is ready, which introduces additional decoherence. Both cases are analysed to capture realistic mismatches between qubit‑preparation rates and entanglement‑generation rates.

The core methodological contribution is the formulation of the hardware‑requirements problem as an optimisation task. Decision variables include memory coherence time, detector efficiency, fiber attenuation, entanglement‑generation success probability, and memory cut‑off timing. By modelling the link‑generation times as order statistics (minimum, maximum, and mean of exponential waiting times), the authors derive closed‑form analytical expressions for (i) the probability of successful end‑to‑end entanglement, (ii) the average entanglement generation time (i.e., rate), and (iii) the expected teleportation fidelity. These formulas explicitly incorporate memory decoherence, swapping delays, and the cut‑off policy, and they are validated against extensive NetSquid simulations, showing agreement within a few percent.

For quantitative evaluation the paper adopts a heterogeneous hardware platform: trapped‑ion processors for the MNs (baseline parameters: memory coherence ≈ 1 s, detector efficiency ≈ 60 %, gate error ≈ 1 %) and ensemble‑based quantum memories for the backbone (baseline: coherence ≈ 0.5 s, retrieval efficiency ≈ 50 %). Optimistic (near‑future) parameter sets are also defined (e.g., coherence up to 10 s, detector efficiency 90 %, retrieval efficiency 80 %).

Four key questions are answered:

• Q1 – With baseline parameters, can teleportation within a single MN exceed the 2/3 fidelity? The answer is yes for ER teleportation; QR requires modest improvements (≈ 30 % longer memory coherence and ≈ 20 % higher detector efficiency).

• Q2 – Assuming the backbone already achieves optimistic performance, what minimal upgrades to MN hardware are needed for intercity teleportation (fidelity ≥ 2/3)? ER remains feasible with only slight MN improvements; QR demands roughly a two‑fold increase in memory coherence and entanglement‑generation success probability.

• Q3 – Conversely, assuming optimistic MN performance, what backbone upgrades are required? The findings mirror Q2: ER works with current MNs, while QR needs significant backbone enhancements (memory coherence ≈ 5 s, retrieval efficiency ≈ 80 %).

• Q4 – With both MN and backbone at baseline, what joint improvements are necessary? Neither ER nor QR can meet the fidelity threshold; a combined upgrade to memory coherence (~5 s), detector efficiency (~0.8), and backbone retrieval efficiency (~0.7) is identified as the minimal set.

Key insights emerging from the analysis are: (1) the ER strategy dramatically lowers hardware demands because it eliminates decoherence of the data qubit during the stochastic entanglement phase; (2) backbone performance has a non‑linear impact on overall teleportation quality, especially when the cut‑off policy is optimised; (3) heterogeneous architectures (trapped‑ion MNs + ensemble repeaters) are realistic and can achieve the target fidelity with plausible near‑term advances; (4) the closed‑form analytical framework enables rapid exploration of the high‑dimensional parameter space without costly simulations, providing a practical tool for quantum‑network designers.

In conclusion, the paper demonstrates that metropolitan‑scale teleportation is already within reach using existing trapped‑ion technology under the ER mode, while extending quantum teleportation to intercity distances requires coordinated improvements in both memory coherence and detection/retrieval efficiencies. The identified hardware targets are modest enough to be attainable in the next few years, offering a concrete roadmap for building the first generation of quantum internet links that can reliably surpass the classical fidelity limit.