论文标题
最佳速度哈密顿演变的Bloch球体上的量子测量学
Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions
论文作者
论文摘要
在量子进化的几何形状中，一条大地路径被视为最小统计长度的路径，连接两个纯量子状态，最大数量的统计上可区分的状态是最小的。在本文中，我们介绍了从单量量子态的量子演化中出现的动力学轨迹的明确测量分析。该进化由冬宫的哈密顿操作员支配，该操作员在给定的初始和最终纯状态之间实现了最快的统一演变。此外，除了将射线空间中的大地学视为最小长度的路径外，我们还根据单位几何效率和消失的几何阶段来验证路径的地球探测性。最后，基于我们的分析，我们简要解决了转向混合量子状态下开放量子系统的量子发展的几何形状的主要障碍。
In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we present an explicit geodesic analysis of the dynamical trajectories that emerge from the quantum evolution of a single-qubit quantum state. The evolution is governed by an Hermitian Hamiltonian operator that achieves the fastest possible unitary evolution between given initial and final pure states. Furthermore, in addition to viewing geodesics in ray space as paths of minimal length, we also verify the geodesicity of paths in terms of unit geometric efficiency and vanishing geometric phase. Finally, based on our analysis, we briefly address the main hurdles in moving to the geometry of quantum evolutions for open quantum systems in mixed quantum states.
