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This research proposes a geometric framework for aligning squeezed states in SU(2)-symmetric systems by treating the squeezing ellipse's orientation as a controllable degree of freedom on the unit sphere. The study demonstrates that optimal measurement-state preparation can be achieved through specific trajectories whose rotation depends on the enclosed solid angle, effectively linking metrological optimization to geometric phases like those seen in Berry phase phenomena. Such methods offer new pathways for enhancing precision measurements across various quantum platforms using polarization-squeezed light and birefringent elements.
On Optimal Measurement-State Preparation via Geometric Transport of the Squeezing Ellipse
arXiv:2607.28620v1 Announce Type: new Abstract: 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.
Abstract: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.
Quantum Physics (quant-ph); Applied Physics (physics.app-ph); Optics (physics.optics)
arXiv:2607.28620 [quant-ph]
(or arXiv:2607.28620v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.28620 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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