AI 中文总结
研究基于量子纠错码的鲁棒逻辑贝尔非定域性，构建逻辑贝尔不等式，证明其对退相干有鲁棒性，对比物理量子比特系统给出相关数据及实现电路，为可扩展逻辑量子系统解锁鲁棒贝尔非定域性及应用提供可行途径。
AI 中文摘要
基于违反类贝尔不等式的量子非定域性是量子物理的基本特征，推动了设备无关量子信息技术的发展。现有贝尔非定域性研究主要集中在物理量子比特系统，其退相干敏感性限制了设备无关应用的性能和安全性。本文研究基于量子纠错码的鲁棒逻辑贝尔非定域性，在稳定子编码子空间构建一般逻辑贝尔不等式，证明其违反表明逻辑系统的全局非定域特征，且该非定域性对退相干具有鲁棒性。通过与物理量子比特系统对比，给出了基于[[3,1,1]]和[[7,1,1]]重复码在比特翻转错误模型下逻辑贝尔不等式违反的保真度阈值等数据，还给出了基于[[3,1,1]]重复码的逻辑贝尔测试实现电路。此工作为在可扩展逻辑量子系统中解锁鲁棒贝尔非定域性提供了可行途径，促进其在未来可扩展量子网络中的应用。
英文摘要
Quantum nonlocality based on the violation of Bell-like inequalities constitutes a fundamental feature of quantum physics and drives the development of device-independent (DI) quantum information technologies. Existing studies of Bell nonlocality have mainly focused on physical qubit systems, where the observed nonlocal correlations are directly encoded in physical degrees of freedom. The decoherence sensitivity of Bell nonlocality largely limits the performance and security of its DI applications. Here, we investigate the robust logical Bell nonlocality based on quantum error correction codes. We construct the general logical Bell inequality in the stabilizer coding subspace and prove its violation indicates the global nonlocal feature of the logical system. Then, we indicate that the logical Bell nonlocality is robust against decoherence. Comparing with the physical qubit system, the fidelity thresholds for the logical Bell inequality violation based on the [[3,1,1]] and [[7,1,1]] repetition codes under the bit-flip error model can be reduced from 82.8% to 73.10% and 66.35%, increasing DI QKD's bit-flip noise threshold from 10.64% to 14.42% and 23.36%, respectively. Such stabilizer-based framework can be also used to characterize the multipartite logical Bell nonlocality in principle. Finally, a logical Bell test implementation circuit based on the [[3,1,1]] repetition code is presented. This work provides a feasible avenue for unlocking robust Bell nonlocality in scalable logical quantum systems and facilitates its applications in future scalable quantum network.
Comments18 pages, 9 figures
