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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
Figure 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
Figure 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
Figure 3. The mapping relationship between W and $ |0\rangle, |1\rangle $.
图 4 网络结构
Figure 4. Network structure.
图 5 量子密钥分发流程图
Figure 5. Quantum key distribution flowchart.
图 6 状态表
Figure 6. State table.
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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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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