稳定子限制下的渐近纠缠隐藏
Asymptotic Entanglement Hiding under Stabilizer Restrictions
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- School of Computer Science and Technology, University of Science and Technology of China（中国科学技术大学计算机科学与技术学院）
- Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
- School of Software Engineering, University of Science and Technology of China（中国科学技术大学软件工程学院）
- Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）
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中文总结 AI 辅助
该研究针对稳定子限制下的纠缠问题，通过量化稳定子可见纠缠构造了无魔法态的渐近纠缠隐藏方案，揭示了纠缠与魔法作为资源的根本分离，明确了稳定子操作提取纠缠的内在限制。
中文摘要 AI 辅助
纠缠是量子信息处理的核心，而稳定子操作是容错量子计算的基础。我们研究在稳定子限制下，有多少纠缠仍保持可见或可蒸馏。我们通过将测量的相对熵纠缠限制在稳定子测量范围内，量化稳定子可见纠缠，从而得到稳定子操作下纠缠蒸馏的逆界。我们展示了无魔法态的渐近纠缠隐藏：我们在每方N个qutrit上构造纯稳定子态的显式凸混合，其无限制的可见纠缠和LOCC可蒸馏纠缠均以Ω(N/log N)的速度增长，而稳定子可见纠缠和稳定子可蒸馏纠缠在N→∞时消失。因此，由稳定子态携带的无限量LOCC可蒸馏纠缠在稳定子限制下可变得渐近不可见且无法蒸馏。我们进一步证明，尽管Haar随机纯态具有大量无限制可见性，其稳定子可见纠缠大概率为O(1)，且当局部维度通过奇素数增长时，稳定子可见纠缠在纠缠Werner态上均匀消失。这些结果揭示了纠缠与魔法作为资源的根本分离，暴露了使用稳定子操作提取纠缠的内在限制。
英文摘要
Entanglement is central to quantum information processing, while stabilizer operations underpin fault-tolerant quantum computation. We ask how much entanglement remains visible or distillable under stabilizer restrictions. We quantify stabilizer-visible entanglement by restricting the measured relative entropy of entanglement to stabilizer measurements, thereby obtaining converse bounds on entanglement distillation under stabilizer operations. We demonstrate magic-free asymptotic entanglement hiding: we construct explicit convex mixtures of pure stabilizer states on $N$ qutrits per party whose unrestricted visible entanglement and LOCC-distillable entanglement both grow as $Ω(N/\log N)$, while their stabilizer-visible and stabilizer-distillable entanglement vanish as $N\to\infty$. Thus, an unbounded amount of LOCC-distillable entanglement carried by stabilizer states can become asymptotically invisible and undistillable under stabilizer restrictions. We further prove that stabilizer-visible entanglement is $O(1)$ with high probability for Haar-random pure states despite extensive unrestricted visibility, and vanishes uniformly over entangled Werner states as the local dimension grows through odd primes. These results reveal a fundamental separation between entanglement and magic as resources, exposing intrinsic limits on entanglement extraction using stabilizer operations.
