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Acta Physica Sinica

Measurement-device-independent quantum key distribution based on the multi-scale entanglement renormalization ansatz

Hong Lai, S. Y. WANG, Zhongrui Huang

Published Jan 1, 2026• 1 citation
Publisher

Abstract

测量设备无关量子密钥分发(Measurement Device Independent Quantum Key Distribution, MDI-QKD)协议因其对测量端攻击的天然免疫性而成为当前量子通信领域的研究热点，但其密钥生成依赖于两个独立光子同时干涉成功，导致成功概率随通信距离增加和信道损耗增大而急剧下降，严重限制了远距离量子通信能力。且一次成功干涉仅能提取 1 比特密钥信息，编码效率较低，使其难以满足高密钥率应用场景的需求。针对这些关键问题，本文提出将多尺度纠缠重整化假设(Multi-scale Entanglement Renormalization Ansatz，MERA)应用于测量设备无关量子密钥分发协议，并设计了三种具体实现方案：基于MERA态第L层压缩单光子态的MDI-QKD、基于MERA态第L-1层压缩纠缠态的MDI-QKD和混合模式下的MDI-QKD。这些方案利用MERA独特的分层压缩结构，每次压缩均显著减少光子数量，最终仅需传输两个甚至单个光子，即可重构出多层包含多个光子的矩阵乘积态(Matrix Product State，MPS)，从而一次性实现多比特的高效密钥生成，极大地减少了量子信道的使用次数。通过动态调整压缩深度，这三种方案能够根据实际网络环境和误码率情况灵活优化量子资源使用效率，避免低层次网络资源的浪费。同时，相比经典MDI-QKD协议每次干涉仅产生1比特密钥，本文提出的方案实现了密钥规模的指数级增长。通过仿真实验，基于MERA第L层压缩单光子的MDI-QKD协议在通信距离为150km时，较经典MDI-QKD协议提高了约22931%的密钥生成率。基于MERA第L-1层压缩纠缠态的MDI-QKD和混合模式下的MDI-QKD协议，在350km处仍能保持10^-11 bit/pulse 的密钥生成率，较经典MDI-QKD协议延长了约 150 km 的有效通信距离。

DOI
10.7498/aps.75.20251450

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测量设备无关量子密钥分发(Measurement Device Independent Quantum Key Distribution, MDI-QKD)协议因其对测量端攻击的天然免疫性而成为当前量子通信领域的研究热点，但其密钥生成依赖于两个独立光子同时干涉成功，导致成功概率随通信距离增加和信道损耗增大而急剧下降，严重限制了远距离量子通信能力。且一次成功干涉仅能提取 1 比特密钥信息，编码效率较低，使其难以满足高密钥率应用场景的需求。针对这些关键问题，本文提出将多尺度纠缠重整化假设(Multi-scale Entanglement Renormalization Ansatz，MERA)应用于测量设备无关量子密钥分发协议，并设计了三种具体实现方案：基于MERA态第L层压缩单光子态的MDI-QKD、基于MERA态第L-1层压缩纠缠态的MDI-QKD和混合模式下的MDI-QKD。这些方案利用MERA独特的分层压缩结构，每次压缩均显著减少光子数量，最终仅需传输两个甚至单个光子，即可重构出多层包含多个光子的矩阵乘积态(Matrix Product State，MPS)，从而一次性实现多比特的高效密钥生成，极大地减少了量子信道的使用次数。通过动态调整压缩深度，这三种方案能够根据实际网络环境和误码率情况灵活优化量子资源使用效率，避免低层次网络资源的浪费。同时，相比经典MDI-QKD协议每次干涉仅产生1比特密钥，本文提出的方案实现了密钥规模的指数级增长。通过仿真实验，基于MERA第L层压缩单光子的MDI-QKD协议在通信距离为150km时，较经典MDI-QKD协议提高了约22931%的密钥生成率。基于MERA第L-1层压缩纠缠态的MDI-QKD和混合模式下的MDI-QKD协议，在350km处仍能保持10^-11 bit/pulse 的密钥生成率，较经典MDI-QKD协议延长了约 150 km 的有效通信距离。
基于量子存储辅助的测量设备无关量子密钥分发（MDI-QKD）协议原理上能有效提升量子密钥分发系统的传输距离和密钥率，但现有三强度诱骗态方案受有限长效应影响严重，仍存在密钥率低、安全传输距离受限等问题。针对以上问题，本文提出了一种基于双参数扫描的量子存储辅助MDI-QKD协议，一方面，通过使用四强度诱骗态方法降低有限长效应的影响；另一方面，结合集体约束模型与双参数扫描算法来优化有限样本下的单光子计数率和相位误码率的估算精度，从而有效提升系统的整体性能。同时，本文开展了相关数值仿真计算，仿真结果显示，本方案与现有其他同类MDI-QKD方案，比如基于存储辅助的三强度诱骗态方案以及不使用存储的四强度诱骗态方案相比，在相同的实验条件下，分别提升了超过30公里和100公里的安全传输距离。因此，本文工作将为未来发展远距离量子通信网络提供重要的参考价值。
量子密钥分发(quantum key distribution，简称QKD)因其具有理论上的无条件安全性而备受关注，但是在实际系统中，QKD会由于设备的非完美性而易受到量子黑客的攻击。测量设备无关(measurement device independent，简称MDI) QKD方案的提出，很好地解决了这一问题。本文首先介绍MDI-QKD协议的最新研究进展和实现原理，总结归纳了协议在实际应用中的优越性与不足，在分析MDI-QKD改进协议的基础上，重点研究提升方案安全密钥生成率的方法并进行理论证明。 Quantum key distribution (QKD) has been paid much attention because of its theoretical uncondi-tional security. However, in the actual system, QKD will be vulnerable to Quantum hackers because of non-perfection of equipment. The proposal of the measurement device independent (MDI) QKD provide a good solution to this problem. In this paper, we firstly introduce the latest research progress and implementation principles of the MDI-QKD protocol. And then, we summarize the advantages and disadvantages of the protocol in the practical application. Based on the analysis of the MDI-QKD improvement protocol, our research is mainly focused on the method of lifting scheme secure key generation rate and theoretical proof.
We assess the overall performance of our quantum key distribution (QKD) system implementing the measurement-device-independent (MDI) protocol using components with varying capabilities such as different single-photon detectors and qubit preparation hardware. We experimentally show that superconducting nanowire single-photon detectors allow QKD over a channel featuring 60 dB loss, and QKD with more than 600 bits of secret key per second (not considering finite key effects) over a 16 dB loss channel. This corresponds to 300 and 80 km of standard telecommunication fiber, respectively. We also demonstrate that the integration of our QKD system into FPGA-based hardware (instead of state-of-the-art arbitrary waveform generators) does not impact on its performance. Our investigation allows us to acquire an improved understanding of the trade-offs between complexity, cost and system performance, which is required for future customization of MDI-QKD. Given that our system can be operated outside the laboratory over deployed fiber, we conclude that MDI-QKD is a promising approach to information-theoretic secure key distribution.
As a multi-particle entangled state, the Greenberger-Horne-Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum keys among multiple users while being resistant to detection attacks. Our simulation results show that the secure distance between each user and the measurement device can reach more than 280 km while reducing the complexity of the quantum network. Additionally, we propose a method to expand our scheme to a multi-node with multi-user network, which can further enhance the communication distance between the users at different nodes.
To date, only active-decoy-state methods have been adopted in current measurement-device-independent (MDI) quantum key distribution (QKD) protocols, causing security loopholes when modulating multiple light intensities with practical devices. To solve this problem, the passive-decoy-state method will be a good choice. Until today practical passive-decoy-state MDI QKD is still missing. In this paper, based on a recently discussed structure of heralded single-photon sources, we propose a passive-decoy-state MDI QKD protocol. In present work, one does not need to modulate light sources into different intensities, but utilizes the built-in local detection events to passively generate different decoy states. Furthermore, through carrying out an appropriate mathematical method, we are able to give very precise estimations for single-photon-pair contributions. As a result, our protocol can exhibit distinct advantages compared with state-of-the-art MDI QKD schemes even when the finite-key-size effect is taken into account. Therefore, our protocol seems a promising candidate to enhance both the security and performance of MDI QKD in practical implementation.
A novel protocol, measurement-device-independent quantum key distribution (MDI-QKD), removes all attacks from the detection system, the most vulnerable part in QKD implementations. In this paper, we present an analysis for practical aspects of MDI-QKD. To evaluate its performance, we study various error sources by developing a general system model. We find that MDI-QKD is highly practical and thus can be easily implemented with standard optical devices. Moreover, we present a simple analytical method with only two (general) decoy states for the finite decoy-state analysis. This method can be used directly by experimentalists to demonstrate MDI-QKD. By combining the system model with the finite decoy-state method, we present a general framework for the optimal choice of the intensities of the signal and decoy states. Furthermore, we consider a common situation, namely asymmetric MDI-QKD, in which the two quantum channels have different transmittances. We investigate its properties and discuss how to optimize its performance. Our work is of interest not only to experiments demonstrating MDI-QKD but also to other non-QKD experiments involving quantum interference.