Heisenberg-scaling measurement of the single-photon Kerr non-linearity using mixed states

Chen, Geng; Aharon, Nati; Sun, Yong-Nan; Zhang, Zi-Huai; Zhang, Wenhao; He, De‐Yong; Tang, Jian‐Shun; Xu, Xiao‐Ye; Kedem, Yaron; Li, Chuan‐Feng; Guo, Guang-Can

doi:10.1038/s41467-017-02487-z

Cited by 43 publications

(25 citation statements)

References 39 publications

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“…It is somewhat surprising that although both pure and mixed probes generate QFI scaling with

, by measuring the meter shift of the successful mode of post-selection, only a mixed probe renders Heisenberg scaling in the estimation of g . An experimental work applies this method to measure the optical Kerr effect in a single photon level [ 21 ], with the setup shown in Figure 3 .…”

Section: Heisenberg Scaling Wm Protocolsmentioning

confidence: 99%

“…For a mixed state, the length can be increased to

, which leads to Heisenberg scaling precision. (Adapted from [ 21 ]).…”

Section: Figurementioning

confidence: 99%

“…Therefore, it is an interesting question to explore the unambiguous advantage of WVA to endow us with unprecedented ability in various measurement tasks. In this review, we will first make an in-depth analysis of the debates between experimentalists and theorists, and then we introduce two advanced weak measurement (WM) protocols [ 21 , 22 ], which beat the standard quantum limit or even approach the Heisenberg limit.…”

Section: Introductionmentioning

confidence: 99%

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Beating Standard Quantum Limit with Weak Measurement

Chen

Yin

Zhang

et al. 2021

Entropy

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Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons.

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“…It is somewhat surprising that although both pure and mixed probes generate QFI scaling with

Section: Heisenberg Scaling Wm Protocolsmentioning

confidence: 99%

“…For a mixed state, the length can be increased to

, which leads to Heisenberg scaling precision. (Adapted from [ 21 ]).…”

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Beating Standard Quantum Limit with Weak Measurement

Chen

Yin

Zhang

et al. 2021

Entropy

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“…Rigorously, this optimization can be achieved by minimizing the number of measurements of n for given values of ϵ and δ. Similar to the realm of quantum metrology 17,18 , an optimal QSV strategy also strives for a 1/n scaling of ϵ, with a minimum constant factor before. For QSV, if the target state is a pure state, the best strategy is the projection onto the target state and its complementary space, then the 1/n scaling is reached, we call this strategy the globally optimal QSV strategy.…”

Section: Introductionmentioning

confidence: 99%

Classical communication enhanced quantum state verification

et al. 2020

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Quantum state verification provides an efficient approach to characterize the reliability of quantum devices for generating certain target states. The figure of merit of a specific strategy is the estimated infidelity ϵ of the tested state to the target state, given a certain number of performed measurements n. Entangled measurements constitute the globally optimal strategy and achieve the scaling that ϵ is inversely proportional to n. Recent advances show that it is possible to achieve the same scaling simply with non-adaptive local measurements; however, the performance is still worse than the globally optimal bound up to a constant factor. In this work, by introducing classical communication, we experimentally implement an adaptive quantum state verification. The constant factor is minimized from ~2.5 to 1.5 in this experiment, which means that only 60% measurements are required to achieve a certain value of ϵ compared to optimal non-adaptive local strategy. Our results indicate that classical communication significantly enhances the performance of quantum state verification, and leads to an efficiency that further approaches the globally optimal bound.

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“…Recently, by considering photon coupling with coherent state pointer, the quantum Fisher information (QFI) can show a quantum scaling of N 2 [18], even without any quantum resources, and soon it was experimentally verified via coherent light as a pointer [19]. Meanwhile, for the mixed states with modulating the power of coherent light, measurement precision can * ligang0311@sina.cn † suiyueqiaoqiao@163.com experimentally attain Heisenberg scaling in weak measurement [20]. Thermal states are real classical states in nature, but they are not considered as the pointers in the original weak measurement protocol because their thermal fluctuations increase with temperature [21].…”

Section: Introductionmentioning

confidence: 99%

Precision metrology of weak measurement with a thermal state pointer

Chen

Wang

et al. 2019

J. Phys. B: At. Mol. Opt. Phys.

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Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after successful postselection can attain the level of thermal fluctuations, without surpassing total QFI, and that QFI which increases with increasing temperature can constantly improve the measurement precision. These results are much better than that of weak measurement with pure state (i.e., Gaussian state) pointer. On the other hand, in Kerr nonlinear interaction systems with weak measurement, and by using thermal state pointer, we obtain in the phase space successful postselection and postselected measurements both achieve the Heisenberg limit of quantum metrology, and show weak measurement with thermal states only obtain classical Fisher information (CFI) which increases with increasing temperature and achieves classical enhanced scaling of N 2 . Moreover, weak measurement with thermal states has an advantage over that with coherent states or mixed states of the light because generating these states with more large uncertainty are limited under the current technology, but thermal states with more large uncertainly are very easy to achieve with increasing temperature in nature, regardless of thermal states of the light or the matter.

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Heisenberg-scaling measurement of the single-photon Kerr non-linearity using mixed states

Cited by 43 publications

References 39 publications

Beating Standard Quantum Limit with Weak Measurement

Beating Standard Quantum Limit with Weak Measurement

Classical communication enhanced quantum state verification

Precision metrology of weak measurement with a thermal state pointer

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