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arXiv:2412.04838

Transfer of Fisher Information in Quantum Postselection Metrology

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

Published Dec 6, 2024• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2412.04838

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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.
Abstract 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 optical coherent states. However, the observed Heisenberg scaling requires a measurement of the distribution of postselection probability, exhibiting no implementation pathway through conventional measurement paradigms. Here, we demonstrate that the output photons can also reach the Heisenberg scale by utilizing the Fisher information transfer effect, while this scenario exhibits enhanced robustness against dephasing noise. 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.
The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful postselection. In this work we show that, rather than the transverse-spatial-wave-function meter typically considered, using the optical coherent state as a meter, the WVA measurement can outperform the conventional measurement not involving the strategy of postselection. We also show that the postselection procedure involved in the WVA scheme can make a mixture of coherent states work better than a pure coherent state with identical average photon numbers. This is in contrast to the main result proved in the absence of postselection. The postselection strategy can also result in the precision of Heisenberg scaling with the photon numbers without using expensive quantum resources. The present work may stimulate further interest in postselection strategy for quantum precision measurements.
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 ignited extensive research and discussions in the field of quantum metrology due to its sufficient potential in quantum measurement applications. Recent studies demonstrate that weak measurement protocols, when integrated with quantum resources, can achieve Heisenberg scaling while maintaining technical noise advantages. However, scenarios involving dephasing noise have not been addressed, as such noise induces rapid degradation of Heisenberg scaling to the standard quantum limit. Here, we incorporate phase fluctuations, a typical dephasing noise, into three Heisenberg-scaling systems. We find that postselection invariably reduces the robustness of quantum systems. Compared to coherent pointer states, squeezed coherent pointer states can exhibit superior resilience against phase fluctuations through appropriate squeezing-parameter optimization. In addition, in entanglement-assisted systems, we can optimize the postselected angle to compensate for Fisher information loss induced by the postselection process. Our findings reveal that weak measurement exhibits inherent limitations in dephasing noise metrology compared to conventional measurement.
The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful post-selection. %% In this work we show that, rather than the Gaussian meter state as typically considered, using the optical coherent state as a meter, the WVA measurement can definitely outperform the conventional measurement not involving the strategy of post-selection. %% We also show that the post-selection procedure involved in the WVA scheme can make a mixture of coherent states work better than a pure coherent state with identical average photon numbers. This is in sharp contrast to the claim proved in the absence of post-selection. The post-selection strategy can also result in the precision of Heisenberg (or even "super-Heisenberg") scaling with the photon numbers, but without using any expensive quantum resources. %% The present work may stimulate further investigations for the potential of the post-selection strategy in quantum precision measurements.
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.