Abstract

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 $\phi - \theta /2$ with a period $\pi$. We show that when $\phi -\theta /2\ \in [ k\pi /2,3k\pi /4 )( k\in \mathbb{Z} )$, 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 $\phi -\theta /2\ \in ( 3k\pi /4,k\pi ]( k\in \mathbb{Z} )$, the optimal estimation accuracy can be acquired only when the DSV state degenerates to a squeezed vacuum state.

© 2021 Optical Society of America

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