On Optimal Measurement-State Preparation via Geometric Transport of the Squeezing Ellipse
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.