Quantum Fisher information and spin squeezing in one-axis twisting model

We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ₀,φ₀> in a one-axis twisting model. Jin et al. New J. Phys. 11 (2009) 073049 found that the spin squeezing sensitively depends on the polar angle θ₀ of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ₀ in the vicinity of π/2 and a near-Heisenberg limit ∝2/N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ₀～π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.