发表机构
InQubator for Quantum Simulation (IQuS) and Department of Physics, University of Washington; Institute for Quantum Information and Matter (IQIM) and Department of Physics, California Institute of Technology（华盛顿大学量子模拟创新中心及物理系; 加州理工学院量子信息与物质研究所及物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对旋转不变散射，推导了所有自旋J的纠缠功率闭式解，并证明非局域量子资源（如纠缠和魔术）的一阶行为仅由到最近非纠缠门的平方投影希尔伯特-施密特距离决定，揭示了资源产生的几何普适性。
AI 中文摘要
弹性散射可以在两个出射粒子的自旋之间产生纠缠和非局域魔术。产生的纠缠和魔术的量编码在S矩阵中，S矩阵是一个作用于两个自旋为J的粒子的联合希尔伯特空间的幺正量子门。先前的工作针对旋转不变的S矩阵，在J=1/2,1,3/2的情况下推导了纠缠功率与散射相移的关系。本文推导了所有J的闭式解。我们进一步证明，一大类非局域量子资源在一阶近似下仅依赖于到最近的非纠缠门的平方投影希尔伯特-施密特距离。这一结论适用于纠缠功率和非局域魔术功率，而资源的选择仅改变整体归一化。这种普适性确立了散射产生资源能力的共同几何起源，与相互作用的细节无关。
英文摘要
Elastic scattering can generate entanglement and non-local magic between the spins of the two outgoing particles. The amount of entanglement and magic produced is encoded in the S-matrix; a unitary quantum gate that acts on the joint Hilbert space of the two spin-J particles. Previous work derived the entanglement power in terms of the scattering phase shifts for rotationally invariant S-matrices with J=1/2,1,3/2. In this paper, a closed form solution is derived for all J. We further prove that a broad class of non-local quantum resources depend to leading order only on the squared projective Hilbert-Schmidt distance from the nearest non-entangling gate. This holds for the entanglement power and non-local magic power, and the choice of resource simply changes the overall normalization. This universality establishes a common geometric origin for the leading resource-generating capacity of scattering, independent of the details of the interaction.
Comments22 pages, 2 figures
