Protecting weak measurements against systematic errors

Pang, Shengshi; Alonso, Jose Raul Gonzalez; Brun, Todd A.; Jordan, Andrew N.

doi:10.1103/physreva.94.012329

Cited by 43 publications

(21 citation statements)

References 78 publications

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“…In practice, this means the device will detect a frequency that is different from the true frequency by some constant offset. In the WVA interferometer, the frequency readout is amplified while the bias offset error is not, so the error is suppressed [43].…”

Section: A Bias Offset Errorsmentioning

confidence: 99%

Precision frequency measurement on a chip using weak value amplification

Steinmetz¹,

Lyons²,

Song³

et al. 2019

Quantum Communications and Quantum Imaging XVII

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We present an integrated design to precisely measure optical frequency using weak value amplification with a multi-mode interferometer. The technique involves introducing a weak perturbation to the system and then post-selecting the data in such a way that the signal is amplified without amplifying the technical noise, as has previously been demonstrated in a free-space setup. We demonstrate the advantages of a Bragg grating with two band gaps for obtaining simultaneous, stable high transmission and high dispersion. We numerically model the interferometer in order to demonstrate the amplification effect. The device is shown to have advantages over both the free-space implementation and other methods of measuring optical frequency on a chip, such as an integrated Mach-Zehnder interferometer.

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Section: A Bias Offset Errorsmentioning

confidence: 99%

Precision frequency measurement on a chip using weak value amplification

Steinmetz¹,

Lyons²,

Song³

et al. 2019

Quantum Communications and Quantum Imaging XVII

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show abstract

“…The degree of this amplification can be quantified by the so-called weak value defined as

, where

and

are the pre-and post-selection states of the QS. When these two state vectors are (nearly) orthogonal, and their overlapping

is small, the weak value can significantly exceed the normal eigenvalue and lead to an amplified meter shift to overcome certain environmental disturbances [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ]. Specifically, the ultra-small transversal shift of a beam can be observed when WVA is introduced [ 10 , 11 ], and the longitudinal optical phase can be precisely measured when an imaginary weak value is explored [ 12 , 13 ]; what is more, the optical Kerr effect in a single-photon level can also be amplified through WVA [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

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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“…There have been several discussions about the effect of technical noise on WVA systems' Fisher information [30]- [35] . Some optimization schemes to improve the measurement performance have been proposed [36] [44]. We start from a more practical perspective, to comprehensively consider the sensitivity and the effects of noises in the experiments, and to quantitatively analyze the measurement precision.…”

Section: Introductionmentioning

confidence: 99%

Pragmatic Implementation With Non-Gaussian Devices of Noise-Limited Weak Value Amplification

Luo

et al. 2021

IEEE Photonics J.

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An effective approach for general measurement based on weak value amplification using non-Gaussian broadband light sources is demonstrated. This scheme can reduce the difficulty of preparing the measurement apparatus and correcting the systematic error caused by the imperfection of device's wave function, thus making the weak-value amplification scheme more convenient and robust for practical field applications. The influence of several common noise sources in a general application based on weak value amplification is analyzed theoretically and examined experimentally. A purely imaginary weak-value phase measurement system is considered for the noise model verification experimentally. In this we show how to optimize the precision of measurement in a unique solution that takes into account the interplay between precision and uncertainty, and explicate the ramifications of such a compromising and pragmatic approach.

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Protecting weak measurements against systematic errors

Cited by 43 publications

References 78 publications

Precision frequency measurement on a chip using weak value amplification

Precision frequency measurement on a chip using weak value amplification

Beating Standard Quantum Limit with Weak Measurement

Pragmatic Implementation With Non-Gaussian Devices of Noise-Limited Weak Value Amplification

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