Quantum Fisher Information for s u(2) Atomic Coherent States and s u(1, 1) Coherent States

Abstract

We investigate quantum Fisher information (QFI) for su(2) atomic coherent states and su(1, 1) coherent states. In this work, we find that for su(2) atomic coherent states, the QFI with respect to \(\vartheta ~(\mathcal {F}_{\vartheta })\) is independent of φ, the QFI with respect to \(\varphi (\mathcal {F}_{\varphi })\) is governed by 𝜗. Analogously, for su(1,1) coherent states, \(\mathcal {F}_{\tau }\) is independent of φ, and \(\mathcal {F}_{\varphi }\) is determined by τ. Particularly, our results show that \(\mathcal {F}_{\varphi }\) is symmetric with respect to 𝜗 = π/2 for su(2) atomic coherent states. And for su(1,1) coherent states, \(\mathcal {F}_{\varphi }\) also possesses symmetry with respect to τ = 0.