AI 中文总结
该研究提出一种几何框架，通过控制压缩椭圆取向的演化，将初始未对准的压缩输入转换为SU(2)对称系统中的测量最优态，其旋转由轨迹立体角决定，可应用于偏振压缩光等物理平台。
AI 中文摘要
最优测量态的制备是利用压缩态的量子计量学的关键要求。我们讨论一种几何框架，该框架将初始未对准的压缩输入转换为SU(2)对称系统中的测量最优态。在该框架内，压缩椭圆的取向构成额外的几何自由度，随平均态在单位球面上沿受控轨迹演化而变化。椭圆的最终旋转由路径的几何结构决定，对于相关的一类变换，其依赖于轨迹所包围的立体角，建立起与几何相位的联系。该框架适用于不同的物理平台，作为具体实例，我们考虑偏振压缩光，并概述一种使用连续变化双折射元件的可能实现方案。
英文摘要
Preparation of optimal measurement states is a key requirement in quantum metrology utilizing squeezed states. We discuss a geometric framework that transforms an initially misaligned squeezed input into a measurement-optimal state in SU(2)-symmetric systems. Within this framework, the orientation of the squeezing ellipse constitutes an additional geometric degree of freedom and evolves as the mean state follows a controlled trajectory on the unit sphere. The resulting rotation of the ellipse is determined by the geometry of the path and, for the relevant class of transformations, depends on the solid angle enclosed by the trajectory, establishing a connection with the geometric phase. The discussed framework is applicable to different physical platforms. As a particular example, we consider polarization-squeezed light and outline a possible implementation using a continuously varying birefringent element.
