Abstract Weak-value amplification employs postselection to enhance the measurement of small parameters of interest. The amplification comes at the expense of reduced success probability, hindering the utility of this technique as a tool for practical metrology. Following other quantum technologies that display a quantum advantage, we formalize a quantum advantage in the success probability and present a scheme based on non-linear collective Hamiltonians that shows a super-extensive growth in success probability while simultaneously displaying an extensive growth in the weak value. We propose an experimental implementation of our scheme.Abstract Weak-value amplification employs postselection to enhance the measurement of small parameters of interest. The amplification comes at the expense of reduced success probability, hindering the utility of this technique as a tool for practical metrology. Following other quantum technologies that display a quantum advantage, we formalize a quantum advantage in the success probability and present a scheme based on non-linear collective Hamiltonians that shows a super-extensive growth in success probability while simultaneously displaying an extensive growth in the weak value. We propose an experimental implementation of our scheme.

arXiv:2012.13749Quantum Science and TechnologyFeb 1, 20223 citations

Phase estimation based on inverse weak-value using a monochromatic light source

Shiwei Xie, Zhaoxue Li, Yan Liu +1 more

Weak-value measurement (WVM) technique, especially the linear WVM technique, has been proved to be useful in high precision metrology. However, the phase shift to be measured is strictly dominated by the input meter, such as the light wavelength and the space position, which are the basic elements of the linear WVM regime. In this work, an inverse WVM technique using a monochromatic light source is presented to achieve precise estimation of the wavelength-independent phase shift. The theoretical analysis in sensitivity and precision indicates that the inverse WVM technique is more applicable to wavelength-independent phase estimation, as compared to the typical linear WVM technique. Furthermore, two possible experimental designs based on the inverse WVM technique are proposed, which may promote the practical applications of this technique in precision metrology.Weak-value measurement (WVM) technique, especially the linear WVM technique, has been proved to be useful in high precision metrology. However, the phase shift to be measured is strictly dominated by the input meter, such as the light wavelength and the space position, which are the basic elements of the linear WVM regime. In this work, an inverse WVM technique using a monochromatic light source is presented to achieve precise estimation of the wavelength-independent phase shift. The theoretical analysis in sensitivity and precision indicates that the inverse WVM technique is more applicable to wavelength-independent phase estimation, as compared to the typical linear WVM technique. Furthermore, two possible experimental designs based on the inverse WVM technique are proposed, which may promote the practical applications of this technique in precision metrology.

Applied Physics ExpressNov 14, 20194 citations

Enhancing metrology sensitivity by weak measurements

Alex Hayat, Amir Feizpour, Aephraim M. Steinberg

SPIE NewsroomDec 29, 20111 citation

Experimentally quantifying the advantages of weak-value-based metrology

Gerardo I. Viza, Julián Martínez-Rincón, G. B. Alves +2 more

We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a Sagnac interferometer with a monitored dark port (the weak-value-based technique), and by focusing the entire beam to a split detector (the standard technique). By introducing controlled external transverse detector modulations and transverse beam deflection momentum modulations, we quantify the mitigation of these sources in the weak-value-based experiment versus the standard focusing experiment. The experiments are compared using a combination of deterministic and stochastic methods. In all cases, the weak-value technique performs the same or better than the standard technique by up to two orders of magnitude in precision for our parameters. We further measure the statistical efficiency of the weak-value-based technique. By postselecting on $1%$ of the photons, we obtain $99%$ of the available Fisher information of the beam deflection parameter.We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a Sagnac interferometer with a monitored dark port (the weak-value-based technique), and by focusing the entire beam to a split detector (the standard technique). By introducing controlled external transverse detector modulations and transverse beam deflection momentum modulations, we quantify the mitigation of these sources in the weak-value-based experiment versus the standard focusing experiment. The experiments are compared using a combination of deterministic and stochastic methods. In all cases, the weak-value technique performs the same or better than the standard technique by up to two orders of magnitude in precision for our parameters. We further measure the statistical efficiency of the weak-value-based technique. By postselecting on $1%$ of the photons, we obtain $99%$ of the available Fisher information of the beam deflection parameter.

arXiv:1410.8461Physical Review ASep 22, 2015118 citations

Nonlinear quantum metrology

Sergio Boixo

Jan 1, 20080 citations

1%

of the photons, we obtain

99%

of the available Fisher information of the beam deflection parameter.