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 the DSV’s metrology. We found that the accuracy limit of parameter estimation is a function of the phase-sensitive parameter ϕ − θ / 2 with a period π . We show that when ϕ − θ / 2 ∈ [ k π / 2 , 3 k π / 4 ) ( k ∈ Z ) , we can obtain the accuracy of parameter estimation approaching the ultimate quantum limit through the use of the DSV state with the larger displacement and squeezing strength, whereas when ϕ − θ / 2 ∈ ( 3 k π / 4 , k π ] ( k ∈ Z ) , the optimal estimation accuracy can be acquired only when the DSV state degenerates to a squeezed vacuum state.