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A building block of quantum repeaters for scalable quantum networks
Wen-Zhao Liu, Ya-Bin Zhou, Jiu-Peng Chen, Bin Wang, Ao Teng, Xiao-Wen Han, Guang-Cheng Liu, Zhi-Jiong Zhang, Yi Yang, Feng-Guang Liu, ChaoHui Xue, Bo-Wen Yang, Jin Yang, Chao Zeng, Du-Ruo Pan, Ming-Yang Zheng, Xing-Jian Zhang, Cao Shen, Yi-Zheng Zhen, You Xiao, Hao Li, Li-Xing You, XiongFeng Ma, Qi Zhao, Feihu Xu, Ye Wang, Yong Wan, Qiang Zhang, Jian-Wei Pan
TL;DR
Long-distance repeater operation requires remote entanglement to persist until a subsequent entanglement round succeeds. The work demonstrates long-distance deterministic entanglement between trapped-ion memories and applies it in a DI-QKD protocol using random measurement settings. Reconciliation (f = 1.122) and privacy amplification: accumulated CHSH and QBER values corresponded to 1,917 secret bits; at 100 km, asymptotic key rate was 0.0974 per round in the infinite-round limit.
Problem
Long-distance repeater operation requires remote entanglement to persist until a subsequent entanglement round succeeds.
Source: Summary and Outlook · p. 11Method
The work demonstrates long-distance deterministic entanglement between trapped-ion memories and applies it in a DI-QKD protocol using random measurement settings.
Source: DI-QKD protocol and results · p. 10, Summary and Outlook · p. 11Results
Reconciliation (f = 1.122) and privacy amplification: accumulated CHSH and QBER values corresponded to 1,917 secret bits; at 100 km, asymptotic key rate was 0.0974 per round in the infinite-round limit.
Source: DI-QKD protocol and results · pp. 10–11Takeaways & Limitations
The demonstrated long-distance entanglement is a building block for quantum repeaters, while the paper reports a positive asymptotic key rate over 100 km.
Source: Summary and Outlook · p. 11, DI-QKD protocol and results · p. 11Thousands-of-kilometres deterministic entanglement will require longer memory coherence, higher generation rates, and multi-node infrastructure; slow multi-wavelength drift compensation remains unavoidable in this implementation.
Source: Summary and Outlook · pp. 11–12
Abstract
from arXiv · showhide
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.
Heralded entanglement between nodes
The link connects two trapped-ion nodes through phase-stabilized single-photon interference, with heralding at an intermediate node. Telecom conversion and combined phase stabilization support high-contrast interference over 10 km of fibre.
Heralded entanglement between nodes
- Each node hosts a single 40Ca+ ion; emitted 393 nm photons are collected, coupled into fibres, and used to entangle the ions’ internal states with photon-number states.Estimated collection efficiency is 9%; measured single-photon efficiencies before frequency conversion are 2.6% for Alice and 2.8% for Bob.Source: Heralded entanglement between nodes · pp. 4–6
- Phase-stabilized single-photon interference at an intermediate node heralds entanglement between the two nodes through detector clicks.The photons travel through quantum frequency conversion and telecom-band fibre to superconducting nanowire single-photon detectors.Source: Heralded entanglement between nodes · p. 5
- Single photons are converted in one step from 393 nm to 1550 nm using a PPLN waveguide and 527 nm pump laser.At 50 mW pump power, filtering reduces conversion noise to 35 cps while combined transmission efficiency is 28%.Source: Heralded entanglement between nodes · p. 6
- Wavelength-division multiplexing suppresses fibre-link phase noise, while time-division multiplexing compensates slow drifts with a weak 393 nm reference pulse.The reference pulse follows a nearly identical path and is applied during Doppler cooling to avoid heating the ions’ motional states.Source: Heralded entanglement between nodes · pp. 6–7
- 0.986 ± 0.005 interference contrast was achieved at the intermediate node using two reference pulses transmitted through a 10 km fibre link.The contrast was measured with both wavelength-division and time-division stabilization implemented.Source: Heralded entanglement between nodes · p. 7
Characterization of Entanglement
The section evaluates whether heralded entanglement remains useful until another link succeeds, and characterizes fidelity, generation rate, and error mechanisms. The average stored-pair fidelity at subsequent-round success is 0.578 ± 0.006.
Characterization of Entanglement
- 2.226 cps is the entanglement generation rate at α = 17%, corresponding to a 450 ms average generation time.The passage identifies a trade-off between protocol-induced errors, governed by α, and generation rate.Source: Characterization of Entanglement · p. 7
- Fρ+ = 0.923 ± 0.012 and Fρ− = 0.910 ± 0.012 are the measured state fidelities at α = 2.5%.Each is compared with its corresponding ideal Bell state, |Ψ+⟩ or |Ψ−⟩.Source: Characterization of Entanglement · p. 8
- 1.2 quantum link efficiency exceeds the 0.83 threshold required for deterministic remote-entanglement delivery.The 550 ± 36 ms coherence time corresponds to a decoherence rate of 1.8 ± 0.1 Hz.Source: Characterization of Entanglement · p. 9
- Independent measurements show that gate errors are dominated by spontaneous emission, with per-gate error probabilities of 6.1 × 10−4 at the Alice node and 5.7 × 10−4 at the Bob node.Source: Characterization of Entanglement · p. 9
- 0.554 ± 0.050 is the entanglement fidelity at 450 ms for α = 17%, and fidelity remains above 0.5 for up to 547 ± 34 ms.The 450 ms point corresponds to the average generation time at that excitation probability.Source: Characterization of Entanglement · p. 9
- 0.578 ± 0.006 is the expected fidelity of a stored Bell pair when the subsequent entanglement round succeeds.This is the probability-weighted average over intervals between consecutive events with the integration window extended to infinity.Source: Characterization of Entanglement · p. 9
DI-QKD protocol and results
The experiment applies device-independent QKD to heralded entanglement over metropolitan-scale fibre links, using random measurement settings for Bell tests and key generation. It distills 1,917 secret bits over 10 km and reports a positive asymptotic key rate at 100 km.
DI-QKD protocol and results
- Random settings X,Y ∈ {0,1} define Bell-test rounds, while X = 0 and Y = 2 define key-generation rounds.The protocol records inputs and outcomes in independent, trusted local classical memories.Source: DI-QKD protocol and results · p. 10
- Across a 10 km fibre link, 405,145 experimental rounds yielded Bell-test S = 2.5758 ± 0.0059 and key-generation Q = 0.0360 ± 0.0006 after approximately two months of data collection.The average entanglement generation rate was 0.291 s^-1 over a valid accumulation time.Source: DI-QKD protocol and results · p. 10
- 1,917 secret bits were distilled from 405,145 experimental rounds over a 10 km fibre link.The accumulated CHSH and QBER values were processed with information reconciliation and privacy amplification.Source: DI-QKD protocol and results · p. 10
- 0.325 per round is the asymptotic key rate approached as the number of entanglement-generation events increases for the 10 km link.The accumulated data correspond to an approximately 4 × 10^-3 key rate per round.Source: DI-QKD protocol and results · p. 11
- 0.0974 per round is the estimated asymptotic key rate for the 100-km implementation, based on 2,799 rounds.The estimate takes the limit of infinitely many key-generation rounds, with their fraction approaching unity.Source: DI-QKD protocol and results · p. 11
Summary and Outlook
The work demonstrates finite-size DI-QKD over 10 km and a positive key rate over 101 km in the asymptotic limit. Reaching thousands of kilometres will require longer memory coherence, faster entanglement generation, and multi-node infrastructure.
Summary and Outlook
- A factor of 5,000 extension in secure distance over previous demonstrations accompanies finite-size DI-QKD over a 10 km link.The demonstration used 400 hours of continuous data collection.Source: Summary and Outlook · p. 11
- More than two orders of magnitude extension in achievable distance accompanies a positive key rate over 101 km in the asymptotic limit.Source: Summary and Outlook · p. 11
- Thousands-of-kilometres deterministic entanglement will require longer memory coherence, a higher entanglement generation rate, and multi-node network infrastructure.Source: Summary and Outlook · p. 11
- Clock-transition ion species or multi-ion memories with decoherence-free-subspace encoding are proposed to extend memory coherence.Source: Summary and Outlook · p. 12
- Optical-cavity-enhanced photon collection or reconfigurable linear ion chains are proposed to increase remote entangling rates.Multiplexing with reconfigurable chains would allow linear enhancement of heralding probability.Source: Summary and Outlook · p. 12
- Slow drift compensation across multiple wavelengths remains unavoidable in the present implementation, while field demonstration requires cross-node optical frequency and phase referencing.The authors identify a frequency comb at each node for local and remote phase referencing as an integral component.Source: Summary and Outlook · p. 12