Finer sub-Planck structures and displacement sensitivity of SU(1,1) circular states

Fuente: arXiv
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Main Authors: Akhtar, Naeem, Peng, Jia-Xin, Aziz, Tariq, Yang, Xiaosen, Wang, Dong
Format: Preprint
Published: 2026
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_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