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

• URL: http://arxiv.org/abs/2602.14752v1
• Date: Mon, 16 Feb 2026 13:54:51 GMT
• Title: Finer sub-Planck structures and displacement sensitivity of SU(1,1) circular states
• Abstract summary: Quantum states with sub-Planck features exhibit sensitivity to phase-space displacements beyond the standard quantum limit.<n>These states are constructed through the superposition of four Perelomov coherent states on the hyperbolic plane.<n>These structures differ in scale along different phase-space directions, resulting in nonuniform sensitivity enhancement.
• Score: 2.9448594387682223
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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