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

  • Vsevolod Salakhutdinov
  • Nikolay Kalinin
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Abstract

Preparation of optimal measurement states is a key requirement in quantum metrology utilizing squeezed states. Besides positioning the mean state, such preparation requires proper alignment of the squeezing ellipse. 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 depends on the chosen trajectory and is linked to the geometric phase through the evolution of the local basis. The discussed framework is applicable to different physical platforms admitting an effective SU(2) description. As a particular example, we consider polarization-squeezed light and outline a possible implementation using a continuously varying birefringent element.

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Cite

BibTeXRIS
BibTeX
@misc{salakhutdinov2026optimal,
  title = {{On Optimal Measurement-State Preparation via Geometric Transport of the Squeezing Ellipse}},
  author = {Vsevolod Salakhutdinov and Nikolay Kalinin},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.28620},
  eprint = {2607.28620},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.28620},
}
RIS
TY  - UNPB
TI  - On Optimal Measurement-State Preparation via Geometric Transport of the Squeezing Ellipse
AU  - Vsevolod Salakhutdinov
AU  - Nikolay Kalinin
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2607.28620
UR  - https://arxiv.org/abs/2607.28620
AB  - Preparation of optimal measurement states is a key requirement in quantum metrology utilizing squeezed states. Besides positioning the mean state, such preparation requires proper alignment of the squeezing ellipse. 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 depends on the chosen trajectory and is linked to the geometric phase through the evolution of the local basis. The discussed framework is applicable to different physical platforms admitting an effective SU(2) description. As a particular example, we consider polarization-squeezed light and outline a possible implementation using a continuously varying birefringent element.
ER  -