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量子密钥分发(Quantum Key Distribution, QKD)技术因其在确保通信安全方面的潜力而备受关注, 但其在大规模网络中的应用受限于量子资源的稀缺性和低效的利用率. 尤其在Ekert91协议中, 尽管利用了纠缠态对进行密钥生成, 实际参与密钥生成的纠缠对数量有限, 导致资源利用率不高. 为了克服这一挑战, 本文提出一种基于多尺度纠缠重整化假设(Multiscale Entanglement Renormalization Ansatz, MERA)的QKD优化方案, 以提高纠缠资源的利用效率. 该方案利用MERA的分层结构和多体态压缩特性, 有效减少量子存储需求, 并显著提升纠缠对的利用率. 实验模拟显示, 在相同的加密请求(1024比特)和物理条件下, 与传统方法相比, 本文的方案节省了124,151对纠缠资源, 既显著提高了资源的利用效率, 又未降低密钥生成过程的安全性, 有助于推动QKD技术在资源受限的环境中进一步发展和应用.
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关键词:
- 量子密钥分发 /
- 多尺度纠缠重整化假设 /
- 资源利用率 /
- 安全性
Quantum Key Distribution (QKD) is a pivotal technology in the field of secure communications, leveraging the principles of quantum mechanics to enable theoretically unbreakable encryption. However, despite its promise, QKD faces significant challenges in achieving large-scale deployment. The primary hurdle lies in the scarcity of quantum resources, especially entangled photon pairs, which are fundamental to protocols such as Ekert91. In traditional QKD implementations, only a fraction of the entangled pairs generated contribute to raw key production, leading to substantial inefficiencies and resource wastage. Addressing this limitation is crucial to the advancement and scalability of QKD networks. This paper introduces an innovative approach to QKD by integrating the Multiscale Entanglement Renormalization Ansatz (MERA), a technique originally developed for many-body quantum systems. By utilizing MERA's hierarchical structure, the proposed method not only improves the efficiency of entanglement distribution but also reduces the consumption of quantum resources. Specifically, MERA compresses many-body quantum states into lower-dimensional representations, allowing for the transmission and storage of entanglement in a more efficient manner. This compression significantly reduces the number of qubits required, optimizing both entanglement utilization and storage capacity in quantum networks. To evaluate the performance of this method, we conducted simulations under standardized conditions. The simulations assumed a 1024-bit encryption request, an 8% error rate, an average path length of 4 hops in the quantum network, and a 95% success rate for both link entanglement generation and entanglement swapping operations. These parameters mirror realistic physical conditions found in contemporary QKD networks. The results demonstrate that the MERA-based approach saves an impressive 124,151 entangled pairs compared to traditional QKD protocols. This substantial reduction in resource consumption underscores the potential of MERA to revolutionize the efficiency of QKD systems without compromising security. Importantly, the security of the key exchange process remains intact, as the method inherently adheres to the principles of quantum mechanics, particularly the no-cloning theorem and the use of randomness in decompression layers. The paper concludes that MERA not only enhances the scalability of QKD by optimizing quantum resource allocation but also maintains the security guarantees essential for practical cryptographic applications. By integrating MERA into existing QKD frameworks, we can significantly lower the resource overhead, making large-scale, secure quantum communication more feasible. These findings contribute a new dimension to the field of quantum cryptography, suggesting that advanced quantum many-body techniques like MERA hold the potential to unlock the full potential of quantum networks in real-world scenarios. 
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Keywords:
- Quantum key distribution /
- Multi-scale entanglement renormalization ansatz /
- Resource utilization /
- Security
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图 1 MERA结构: (a) 二元MERA; (b) 三元MERA; (c) 解纠缠算符U; (d) 等距映射W
Fig. 1. The structure of MERA: (a) Binary MERA; (b) Ternary MERA; (c) Disentangling operator U; (d) Isometric mapping W.
图 2 U与$ |00\rangle, |01\rangle, |10\rangle, |11\rangle $的映射关系
Fig. 2. The mapping relationship between U and $ |00\rangle, |01\rangle, |10\rangle, |11\rangle $.
图 3 W与$ |0\rangle, |1\rangle $的映射关系
Fig. 3. The mapping relationship between W and $ |0\rangle, |1\rangle $.
图 7 传统方式与MERA方式下量子资源消耗随需求变化的关系
Fig. 7. Relationship between quantum resource consumption and demand in traditional versus MERA.
图 8 传统方式与MERA方式下经典资源消耗随需求变化的关系
Fig. 8. Relationship between classical resource consumption and demand in traditional versus MERA.
图 9 传统方式与MERA方式下总资源消耗随需求变化的关系
Fig. 9. The relationship between total resource consumption and demand in traditional versus MERA.
图 10 所需量子资源随平均路径跳数从1到10的变化情况
Fig. 10. Variation in quantum resource requirements as average path length increases from 1 to 10.
图 11 平均路径跳数为4、5、6时, 量子资源消耗随请求量的变化
Fig. 11. Quantum Resource Variation with Request Volume at Average Path Lengths of 4, 5, and 6.
图 12 误码率从1%—10%变化时, 所需量子资源的增长情况
Fig. 12. Variation in Quantum Resource Requirements as Error Rate Changes from 1% to 10%.
图 13 误码率为7%、8%、9%时, 量子资源随请求量变化的情况
Fig. 13. Quantum Resource Variation with Request Volume at Error Rates of 7%, 8%, and 9%.
图 14 链路纠缠成功率从70%到95%变化时, 所需量子资源数量的变化趋势
Fig. 14. Quantum Resource Variation as Link Entanglement Success Rate Ranges from 70% to 95%.
图 15 链路纠缠成功率分别取85%、90%、95%时, 量子资源的变化趋势
Fig. 15. Quantum Resource Variation at Link Entanglement Success Rates of 85%, 90%, and 95%.
图 16 纠缠交换成功率从70%到95%变化时, 所需量子资源数量的变化趋势
Fig. 16. Quantum Resource Variation as Entanglement Swapping Success Rate Ranges from 70% to 95%.
图 17 纠缠交换成功率为85%、90%、95%时, 量子资源的变化趋势
Fig. 17. Quantum Resource Variation at Entanglement Swapping Success Rates of 85%, 90%, and 95%.
表 1 网络请求属性及其取值范围
Table 1. Network request attributes and their value ranges.
属性 描述 取值范围 S 发送方 N/A D 接收方 N/A k 需求量 $ [1024, 4096] $ P 优先级 $ [1, 5] $ $ \Delta t $ 可接受时延 $ [1, 60] $ 
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