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arXiv:1611.07328 · Physical Review A

Optimal conventional measurements for quantum-enhanced interferometry

Wei Zhong, Yixiao Huang, Xiaoguang Wang, Shi-Liang Zhu

Published May 2, 2017• 18 citations
arXivHTMLPDF

Abstract

A major obstacle to attaining the fundamental precision limit of phase estimation in interferometry is the identification and implementation of the optimal measurement. Here we demonstrate that this can be accomplished by the use of three conventional measurements among interferometers with Bayesian estimation techniques. Conditions that hold for the precision limit to be attained with these measurements are obtained by explicitly calculating the Fisher information. Fortunately, these conditions are naturally satisfied in most interferometric experiments. We apply our results to an atomic spectroscopy experiment and examine the robustness of phase sensitivity for the two-axis counter-twisted state suffering from detection noise.

DOI
10.1103/physreva.95.052304

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A major obstacle to attaining the fundamental precision limit of phase estimation in interferometry is the identification and implementation of the optimal measurement. Here we demonstrate that this can be accomplished by the use of three conventional measurements among interferometers with Bayesian estimation techniques. Conditions that hold for the precision limit to be attained with these measurements are obtained by explicitly calculating the Fisher information. Fortunately, these conditions are naturally satisfied in most interferometric experiments. We apply our results to an atomic spectroscopy experiment and examine the robustness of phase sensitivity for the two-axis counter-twisted state suffering from detection noise.
With the rapid development of quantum technologies in recent years, the need for high-sensitivity measuring techniques has become a key issue. In particular, optical sensors based on quantum states of light have proven to be optimal resources for high-precision interferometry. Nevertheless, their performance may be severely affected by the presence of noise or imperfections. In this work, we derive the quantum Fisher information matrix associated with the simultaneous estimation of an interferometric phase and the indistinguishability characterizing the probe state consisting of an even number of photons. We find the optimal measurement attaining the ultimate precision for both parameters in a single setup and perform an experiment based on a pair of photons with an unknown degree of indistinguishability entering a two-port interferometer.
We consider an optical interferometer with coherent light in one input and a squeezed vacuum in another. Such an interferometer is known to beat the standard quantum limit of sensitivity to the difference of phase shifts in its arms. We find the ultimate limit of precision for such an interferometer by calculating the quantum Fisher information of the mixed quantum state in one of the interferometer's outputs about the difference phase. We show that, in the vicinity of the black fringe, this information is asymptotically close to the quantum Fisher information about this phase for the two-mode readout. We conclude that the single-mode readout is optimal for phase estimation in squeezing-enhanced interferometry and allows for the Heisenberg scaling of precision. We also show that the optimal local measurement in the vicinity of the black fringe consists of amplifying the output field in a phase-sensitive way and measuring its photon number.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.
Quantum parameter estimation utilizes quantum mechanical effects to attain higher measurement precision than classical schemes. In practical implementations, however, noise is inevitably present during the measurement process, causing a decrease in precision. Quantifying the impact of noise on different measurements is of considerable significance. Here, we experimentally investigate robust optimal measurements based on the theory of Fisher information measurement noise susceptibility (FI MENOS), which quantifies how susceptible a measurement is to noise. By constructing a polarizing Mach-Zehnder interferometer, we implement phase estimation under controlled noise. Our results indicate that different measurements exhibit distinct sensitivities to noise. To assess the influence of diverse noise types on precision, we further construct an experimental setup capable of introducing various forms of noise. The experimental results affirm that FI MENOS represents the worst-case scenario for estimation precision, enabling us to evaluate the noise immunity of optimal measurements. Our work provides a deeper insight into quantum metrology with noise, marking a notable advancement in quantifying the robustness of quantum estimation schemes against measurement noise effects.
Spin-squeezed states constitute a valuable entanglement resource capable of surpassing the standard quantum limit (SQL). However, spin-squeezed states only enable sub-SQL uncertainty within a narrow parametric window near some specific points. Identifying optimal measurement protocols for spin-squeezed states remains an outstanding challenge. Here we present an adaptive Bayesian quantum estimation protocol that achieves optimal measurement precision with spin-squeezed states under noises. Our protocol operates by maintaining measurements near the optimal point and employing Bayesian inference to sequentially perform phase estimation, enabling robust high-precision measurement. To account for realistic experimental conditions, we explicitly incorporate phase noises into the Bayesian likelihood function for more accurate estimation. Our protocol can be applied to various scenarios, such as quantum gravimeters and atomic clocks, achieving precision enhancement over conventional fitting methods under noises. Our approach offers superior precision and enhanced robustness against noises, making it highly promising for squeezing-enhanced quantum sensing.
Abstract Photon counting measurement has been regarded as the optimal measurement scheme for phase estimation in the squeezed-state interferometry, since the classical Fisher information equals to the quantum fisher information and scales as n ¯ 2 for given input number of photons n ¯ . However, it requires photon-number-resolving detectors with a large enough resolution threshold. Here we show that a collection of N -photon detection events for N up to the resolution threshold ∼ n ¯ can result in the ultimate estimation precision beyond the shot-noise limit. An analytical formula has been derived to obtain the best scaling of the fisher information.