Phase-sensitive nonclassical properties in quantum metrology with a displaced squeezed vacuum state

We predict that the phase-dependent error distribution of locally unentangled quantum states directly affects quantum parameter estimation accuracy. Therefore, we employ the displaced squeezed vacuum (DSV) state as a probe state and investigate an interesting question of the phase-sensitive nonclassical properties in DSVs metrology. We found that the accuracy limit of parameter estimation is a function of the phase-sensitive parameter $phi -theta /2$ with a period $pi $. We show that when $phi -theta /2$ $in left[ kpi/2,3kpi /4right) left( kin mathbb{Z}right)$, we can obtain the accuracy of parameter estimation approaching the ultimate quantum limit through using the DSV state with the larger displacement and squeezing strength, whereas $phi -theta /2$ $in left(3kpi /4,kpi right] left( kin mathbb{Z}right) $, the optimal estimation accuracy can be acquired only when the DSV state degenerates to a squeezed-vacuum state.