Finer sub-Planck structures and displacement sensitivity of SU(1,1) circular states
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910023815266304 |
|---|---|
| author | Akhtar, Naeem Peng, Jia-Xin Aziz, Tariq Yang, Xiaosen Wang, Dong |
| author_facet | Akhtar, Naeem Peng, Jia-Xin Aziz, Tariq Yang, Xiaosen Wang, Dong |
| contents | Quantum states with sub-Planck features exhibit sensitivity to phase-space displacements beyond the standard quantum limit, making them useful for quantum metrology. In the context of the SU(1,1) group, sub-Planck features have been constructed through the superposition of four Perelomov coherent states on the hyperbolic plane (the SU(1,1) compass state). However, these structures differ in scale along different phase-space directions, resulting in nonuniform sensitivity enhancement. We overcome this limitation by constructing $\overline{n}$-component compass states, which are obtained by superposing $\overline{n} \geq 6$ SU(1,1) coherent states, with an even total number, evenly arranged along a circular path on the hyperbolic plane; that is, all components lie at the same distance from the origin and have equal angular spacing of $\frac{2π}{\overline{n}}$. These generalized SU(1,1) compass states generate circularly shaped sub-Planck features (isotropic sub-Planckness) and provide uniform enhancement in sensitivity to phase-space displacements. As the number of coherent states $\overline{n}$ increases, these refinements progressively improve. While verified for $\overline{n} = 16$ SU(1,1) coherent states, the results remain valid for superpositions with arbitrarily large $\overline{n}$ components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14752 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finer sub-Planck structures and displacement sensitivity of SU(1,1) circular states Akhtar, Naeem Peng, Jia-Xin Aziz, Tariq Yang, Xiaosen Wang, Dong Quantum Physics Quantum states with sub-Planck features exhibit sensitivity to phase-space displacements beyond the standard quantum limit, making them useful for quantum metrology. In the context of the SU(1,1) group, sub-Planck features have been constructed through the superposition of four Perelomov coherent states on the hyperbolic plane (the SU(1,1) compass state). However, these structures differ in scale along different phase-space directions, resulting in nonuniform sensitivity enhancement. We overcome this limitation by constructing $\overline{n}$-component compass states, which are obtained by superposing $\overline{n} \geq 6$ SU(1,1) coherent states, with an even total number, evenly arranged along a circular path on the hyperbolic plane; that is, all components lie at the same distance from the origin and have equal angular spacing of $\frac{2π}{\overline{n}}$. These generalized SU(1,1) compass states generate circularly shaped sub-Planck features (isotropic sub-Planckness) and provide uniform enhancement in sensitivity to phase-space displacements. As the number of coherent states $\overline{n}$ increases, these refinements progressively improve. While verified for $\overline{n} = 16$ SU(1,1) coherent states, the results remain valid for superpositions with arbitrarily large $\overline{n}$ components. |
| title | Finer sub-Planck structures and displacement sensitivity of SU(1,1) circular states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.14752 |