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arXiv:2105.00970 · Journal of the Optical Society of America B

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

Zhiwei Tao, Yi-Chong Ren, Azezigul Abdukirim, Shiwei Liu, Ruizhong Rao

Published Mar 30, 2021• 1 citation
arXivHTMLPDF

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 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.

DOI
10.1364/josab.419752

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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.
Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of [ 0 , π / 2 ) . Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from [ 0 , π ) , where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology.
We investigate the nonclassical properties of multiple-photon-added displaced squeezed thermal states (PADSTSs). Particularly, we study the dependence of those nonclassical properties on the compound phase ϕ−θ/2 involved in squeezing and displacement parameters. We find that the Mandel Q parameter, the quadrature squeezing, the negative volume of the Wigner function, and the fidelity between PADSTSs and displaced squeezed thermal states (DSTSs) are all periodic functions of ϕ−θ/2 with a period π. Without considering the displacement parameter, these quantities are all phase independent. Finally, we investigate the non-Gaussianity of PADSTSs according to the fidelity between PADSTSs and DSTSs and find that non-Gaussianity and nonclassicality have similar behavior. Thus, the non-Gaussianity induced by the photon-addition operation is essentially nonclassical.
Quantum phase-estimation protocols can provide a measuring method of phase shift with precision superior to the standard quantum limit (SQL) due to the application of a nonclassical state of light. A squeezed vacuum state, whose variance in one quadrature is lower than the corresponding SQL, has been pointed out as a sensitive resource for quantum phase estimation and the estimation accuracy is directly influenced by the properties of the squeezed state. Here we analyze in detail the influence of the purity and squeezing level of the squeezed state on the accuracy of quantum phase estimation. The maximum precision that can be achieved for a squeezed thermal state is evaluated, and the experimental results are in agreement with the theoretical analyses. It is also found that the width of the phase-estimation interval $\mathrm{\ensuremath{\Delta}}\ensuremath{\theta}$ beyond SQL is correlated with the purity of the squeezed state.
Abstract The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators X^P^+P^X^\hat X\hat P + \hat P\hat XX^P^+P^X^ X ̂ P ̂ + P ̂ X ̂ , i.e., a non-Gaussian measurement, is required to be fully optimal.