AI 中文总结
研究魔法与纠缠在多体动力学中的关系，揭示两个结构原理，通过克利福德剪枝电路等方法构造特定族，求解伊辛猝灭和踢弗洛凯链，验证预测并给出检测魔法的协议，展现魔法与纠缠的不同特性。
AI 中文摘要
魔法和纠缠是独立的量子资源，但其在多体动力学中的确切关系仍不清楚。我们揭示了两个结构原理。一是在任何稳定器状态下，任意厄米生成器作用下第二个稳定器雷尼熵的曲率与量子费舍尔信息在固定归一化下相等，建立了计算资源和计量资源之间的双向桥梁。二是对于任何森林图上的对易伊辛演化，一个克利福德剪枝电路能在任意大小和任意空间嵌入下产生完整的稳定器 - 雷尼族，从而在热力学极限下提供了具有有限魔法密度和零纠缠密度的族的图论构造。我们精确求解了量子模拟中两个典型的一维实现——伊辛猝灭和踢弗洛凯链，揭示了有限魔法密度和零纠缠密度、不同的魔法和纠缠复苏周期以及具有零魔法但有限二分纠缠量的克利福德点。相同的切几何确定了初始增长、微扰复苏提升和热力学魔法极小值的稳定性。大规模泡利基矩阵乘积态计算验证了所有预测，切桥给出了通过已有的量子费舍尔信息测量检测魔法的具体协议。
英文摘要
Magic and entanglement are independent quantum resources, yet their exact relation in many-body dynamics has remained elusive. We uncover two structural principles. First, at any stabilizer state, the curvature of the second stabilizer Rényi entropy under an arbitrary Hermitian generator equals the quantum Fisher information up to a fixed normalization, creating a bidirectional bridge between computational and metrological resources. Second, for commuting Ising evolution on any forest graph, a Clifford pruning circuit yields the full stabilizer-Rényi family at arbitrary size and in any spatial embedding, thereby furnishing a graph-theoretic construction of families with finite magic density and vanishing entanglement density in the thermodynamic limit. We solve two paradigmatic one-dimensional realizations central to quantum simulation -- an Ising quench and a kicked Floquet chain -- exactly for arbitrary system size and directly in the thermodynamic limit, revealing finite magic density with vanishing entanglement density, distinct magic and entanglement revival periods, and Clifford points with zero magic but finite bipartite entanglement. The same tangent geometry fixes initial growth, perturbative revival lifting, and stability of thermodynamic magic minima. Large-scale Pauli-basis matrix-product-state calculations verify all predictions, and the tangent bridge yields a concrete protocol for detecting magic through established quantum-Fisher-information measurements.
Comments6+42 pages, 3+0 figures
