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Physical Review A

Fisher information analysis on weak-value-amplification metrology using optical coherent states

Yingxin Liu, Lupei Qin, Xin-Qi Li

Published Aug 30, 2022• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.106.022619

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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.
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.
Weak-value amplification (WVA) has emerged as an effective technique for detecting extremely small physical parameters by combining weak system–meter interactions with a carefully chosen post-selection strategy. In this paper, we explore how WVA performs when the meter is prepared in a Schrödinger cat-like state (SCS). Using the Fisher information (FI) as the primary figure of merit, we assess the attainable precision in estimating the interaction parameter. We compare the sensitivities of even coherent states (ECSs), odd coherent states (OCSs), and Yurke–Stoler states (YSSs) against coherent states (CS). We demonstrate that ECS and OCS as meters provide higher FI than the CS as a meter in some cases, depending on the measurement strategy. Also, ECS yields the largest conventional FI among the four meter states. Furthermore, we explore the impact of vacuum superposition with the meter on FI. We find that optimizing the vacuum coefficient enhances the FI in some conditions. This study shows that SCSs can be useful as meter states for improving precision in weak-measurement 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.
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.
Weak-value amplification (WVA) provides a way for amplified detection of a tiny physical signal at the expense of a lower detection probability. Despite this trade-off, due to its robustness against certain types of noise, WVA has advantages over conventional measurements in precision metrology. Moreover, it has been shown that WVA-based metrology can reach the Heisenberg limit using entangled resources, but preparing macroscopic entangled resources remains challenging. Here, we demonstrate a novel WVA scheme based on iterative interactions, achieving the Heisenberg-limited precision scaling without resorting to entanglement. This indicates that the perceived advantages of the entanglement-assisted WVA are in fact due to iterative interactions between each particle of an entangled system and a meter, rather than coming from the entanglement itself. Our work opens a practical pathway for achieving the Heisenberg-limited WVA without using fragile and experimentally demanding entangled resources.
Abstract Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.