量子比特系统中由量子通道诱导的Uhlmann相位几何
Quantum Channel-Induced Geometry of the Uhlmann Phase in Qubit Systems
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中文总结 AI 辅助
该研究揭示了循环控制的非相干生成量子通道诱导双参数Bloch轨迹，使纯态量子比特获得非平凡Uhlmann相位，缺陷动力学驱动局域几何跃迁，与单参数热Uhlmann跃迁机制不同。
中文摘要 AI 辅助
我们证明，循环控制的非相干生成通道提供了双参数族的闭合Bloch轨迹，这在热Uhlmann文献的单参数（温度）循环中是不存在的，其关联的Uhlmann相位在通道参数环面上形成了真实的涡旋-反涡旋结构。制备于纯态的量子比特自身不携带几何相位，它获得的非平凡Uhlmann相位（此处以闭合形式求得）完全源自本征量子通道参数空间中的闭合回路。根据Poincaré-Hopf定理，这些缺陷的净拓扑荷被约束为零。当输入态取向趋近于其临界值时，缺陷遵循平方根合并定律成对合并并湮灭。这种缺陷动力学驱动了局域几何跃迁，该机制与单参数热Uhlmann跃迁形成对比，后者中全局量子化的缠绕数作为体不变量发生跳跃。
英文摘要
We show that a cyclically controlled non-coherence-generating channel supplies a two-parameter family of closed Bloch trajectories, absent in the single-parameter (temperature) cycles of the thermal Uhlmann literature, whose associated Uhlmann phase develops a genuine vortex--antivortex structure on the channel-parameter torus. A qubit prepared in a pure state, which carries no geometric phase of its own, acquires a nontrivial Uhlmann phase, obtained here in closed form, purely from a closed loop in the space of the native quantum channel parameters. The net topological charge of these defects is constrained to zero by the Poincaré--Hopf theorem. As the input-state orientation approaches its critical values, the defects merge and annihilate in pairs following a square-root coalescence law. This defect dynamics drives local geometric transitions, a mechanism that contrasts with single-parameter thermal Uhlmann transitions, where a global quantized winding jumps as a bulk invariant.
