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Journal of the Optical Society of America B

Entanglement-assisted cyclic weak-value-amplification metrology

Zi-Rui Zhong, Xia-Lin Su, Ke-Xuan Chen, Huilin Xu, Yan Zhang, Xiangming Hu, Qing-Lin Wu

Published Apr 29, 2025• 2 citations
Publisher

Abstract

Weak measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and signal-to-noise ratio (SNR) of weak measurement from distinct perspectives. Here, we incorporate a power-recycling cavity into the entanglement-assisted weak measurement system. We obtain an improvement of both detection efficiency and Fisher information, driven by the combined effects of power cycling and entanglement. Furthermore, we analyze three types of errors: cavity power loss, walk-off errors, and readout errors. The conclusions suggest that entanglement is beneficial in mitigating the effects of cavity losses. Moreover, entanglement exacerbates the walk-off effect caused by recycling, but this detriment can be balanced by proper parameter selection. Additionally, power-recycling can complement entanglement in suppressing readout noise, thus enhancing the accuracy of the measurement results and recovering the lost Fisher information. This work delves deeper into the metrological advantages of weak measurement.

DOI
10.1364/josab.545477

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Weak measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and signal-to-noise ratio (SNR) of weak measurement from distinct perspectives. Here, we incorporate a power-recycling cavity into the entanglement-assisted weak measurement system. We obtain an improvement of both detection efficiency and Fisher information, driven by the combined effects of power cycling and entanglement. Furthermore, we analyze three types of errors: cavity power loss, walk-off errors, and readout errors. The conclusions suggest that entanglement is beneficial in mitigating the effects of cavity losses. Moreover, entanglement exacerbates the walk-off effect caused by recycling, but this detriment can be balanced by proper parameter selection. Additionally, power-recycling can complement entanglement in suppressing readout noise, thus enhancing the accuracy of the measurement results and recovering the lost Fisher information. This work delves deeper into the metrological advantages of weak measurement.
Weak measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and signal-to-noise ratio (SNR) of weak measurement from distinct perspectives. Here, we incorporate a power recycling cavity into the entanglement-assisted weak measurement system. We obtain an improvement of both detection efficiency and Fisher information, and find that the improvement from entanglement and recycling occur in different dimensions. Furthermore, we analyze two types of errors, walk-off errors and readout errors. The conclusions suggest that entanglement exacerbates the walk-off effect caused by recycling, but this detriment can be balanced by proper parameter selection. In addition, power-recycling can complement entanglement in suppressing readout noise, thus enhancing the accuracy in the measurement results and recovering the lost Fisher information. This work delves deeper into the metrological advantages of weak measurement.
Postselected weak measurement has aroused broad interest for its distinctive ability to amplify small physical quantities. However, the low postselection efficiency to obtain a large weak value has been a big obstacle to its application in practice, since it can waste resources, and reduce the measurement precision. In this paper, we detail the entanglement-assisted postselected weak measurement protocol proposed in [Phys. Rev. Lett. 113, 030401 (2014)], and study its robustness against technical noises. We show that when the systems are properly entangled, postselection can be made dramatically more efficient, and as a consequence, the Fisher information can be increased to approximately saturate the well-known Heisenberg limit. We illustrate this protocol by a qubit example. Readout errors can greatly degrade the performance of postselected weak measurement schemes. We show that entanglement can significantly reduce two main detrimental effects of readout errors: inaccuracy in the measurement result, and loss of the Fisher information. We further compensate for readout errors by a majority vote scheme for postselection. With a proper threshold, almost no Fisher information will be lost. These results demonstrate the effectiveness of entanglement in protecting postselected weak measurement against readout errors.
Postselected weak measurement has aroused broad interest for its distinctive ability to amplify small physical quantities. However, the low postselection efficiency to obtain a large weak value has been a big obstacle to its application in practice since it may waste resources, and reduce the measurement precision. An improved protocol was proposed in Pang et al., Phys. Rev. Lett. 113, 030401 (2014) to make the postselected weak measurement dramatically more efficient by using entanglement. Such a protocol can increase the Fisher information of the measurement to approximately saturate the well-known Heisenberg limit. In this paper, we review the entanglement-assisted protocol of postselected weak measurement in detail, and study its robustness against technical noises. We focus on readout errors. Readout errors can greatly degrade the performance of postselected weak measurement, especially when the readout error probability is comparable to the postselection probability. We show that entanglement can significantly reduce the two main detrimental effects of readout errors: inaccuracy in the measurement result and the loss of Fisher information. We extend the protocol by introducing a majority vote scheme to postselection to further compensate for readout errors. With a proper threshold, almost no Fisher information will be lost. These results demonstrate the effectiveness of entanglement in protecting postselected weak measurement against readout errors.
Weak value amplification permits small effects to be measured as observable changes at the sacrifice of power due to postselection. The power-recycling scheme has been proven to eliminate this inefficiency of the rare postselection, thus surpassing the limit of the shot noise and improving the precision of the measurement. However, the improvement is strictly limited by the system setup, especially the system loss. Here we introduce a dual-recycling model based on the interferometric weak-value-based deflection measurement. Two mirrors, the power-recycling mirror and signal-recycling mirror, are placed at the bright and dark port of the interferometer, respectively, creating a composite resonator. The results show that both the power and the signal-to-noise ratio (SNR) are greatly enhanced in a wider range of experimental parameters compared to the power-recycling scheme. This work considerably loosens the constraint of the system setup and further explores the real advantage of weak measurement over traditional schemes.
The weak-value-based metrology is very promising and has attracted a lot of attention in recent years because of its remarkable ability in signal amplification. However, it is suggested that the upper limit of the precision of this metrology cannot exceed that of classical metrology because of the low sample size caused by the probe loss during postselection. Nevertheless, a recent proposal shows that this probe loss can be reduced by the power-recycling technique, and thus enhance the precision of weak-value-based metrology. Here we experimentally realize the power-recycled interferometric weak-value-based beam-deflection measurement and obtain the amplitude of the detected signal and white noise by discrete Fourier transform. Our results show that the detected signal can be strengthened by power recycling, and the power-recycled weak-value-based signal-to-noise ratio can surpass the upper limit of the classical scheme, corresponding to the shot-noise limit. This work sheds light on higher precision metrology and explores the real advantage of the weak-value-based metrology over classical metrology.
Postselected weak measurement has shown significant potential for detecting small physical effects due to its unique weak-value-amplification phenomenon. Previous works suggest that Heisenberg-limit precision can be attained using only the optical coherent states. However, the measurement object is the distribution of postselection, limiting the practical applicability. Here, we demonstrate that the output photons can also reach the quantum scale by utilizing the Fisher information transfer effect. In addition, we consider the insertion of a power-recycling cavity and demonstrate its positive impact on the distribution of postselection. Our results enhance the quantum metrological advantages of the postselection strategy and broaden its application scope.