Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optimal Metagrating for Position Metrology under Poisson Shot Noise

Zheng Xi, Sander Konijnenberg, Hendrik Paul Urbach

Published Apr 23, 2019• 0 citations
OpenAlex

Abstract

We introduce an optimal metagrating design for position metrology under Poisson shot noise. By using proper electric and magnetic resonances inside the metagrating, the position of the metagrating within an interference field can be extracted with high precision in the presence of shot noise, leading to nearly three orders of magnitude improvement compared to the centroid-fitting-based position metrology with the same number of detected photons. Furthermore, we find that the improvement in precision is closely related to the formation of a phase vortex around the optimal design in the parameter space. The link between the metagrating design, the formation of a phase vortex and the fundamental precision limit using classical light gives new insights to all of these fields.

Related papers

Information-Efficient Metagrating for Transverse-Position Metrology

Zheng Xi, Sander Konijnenberg, Hendrik Paul Urbach

We introduce an optimal metagrating design for transverse-position metrology in presence of photon shot noise. The proposed working principle is closely related to the formation of a phase vortex in the diffraction orders in the parameter space. Using the topological robustness, we optimize the design and compress all the transverse-position information around a certain point into a small number of detected photons, saturating the shot-noise limit had all the photons used for probing the position been detected. The current scheme avoids the problem of detector saturation in the presence of high probe power while maintaining all the information detected, allowing one to make full use of the high power that is available. Besides, the direct link between the resonant property in the unit cell and the conditions to achieve the bound is given: one with the zeroth dipole resonance and the other one with the anapole condition of the first dipole. The connection between the metagrating design and the optimization using topological robustness along with the fundamental precision limit using classical light gives new insights in all of these fields.

arXiv:1904.10486•Physical Review Applied•Jul 9, 2020•10 citations

Optimal Mueller matrix estimation in the presence of additive and Poisson noise for any number of illumination and analysis states

François Goudail

We investigate the optimal strategies for estimating the Mueller matrix with arbitrary numbers of illumination and analysis states, in the presence of signal-independent additive noise or signal-dependent Poisson shot noise. We demonstrate that the architectures that minimize and equalize the estimation variances for both types of noise sources are based on spherical designs of order 2 or 3, and we provide closed-form expressions of the estimation precision obtained with these optimal measurement strategies. The obtained results are important to design Mueller polarimeters in practice and assess their fundamental limits in terms of estimation precision.

Optics Letters•May 26, 2017•19 citations

Optical implementation of spin squeezing

Takafumi Ono, Javier Sabines-Chesterking, Hugo V. Cable +2 more

Quantum metrology enables estimation of optical phase shifts with precision beyond the shot-noise limit. One way to exceed this limit is to use squeezed states, where the quantum noise of one observable is reduced at the expense of increased quantum noise for its complementary partner. Because shot-noise limits the phase sensitivity of all classical states, reduced noise in the average value for the observable being measured allows for improved phase sensitivity. However, additional phase sensitivity can be achieved using phase estimation strategies that account for the full distribution of measurement outcomes. Here we experimentally investigate a model of optical spin-squeezing, which uses post-selection and photon subtraction from the state generated using a parametric downconversion photon source, and we investigate the phase sensitivity of this model. The Fisher information for all photon-number outcomes shows it is possible to obtain a quantum advantage of 1.58 compared to the shot-noise value for five-photon events, even though due to experimental imperfection, the average noise for the relevant spin-observable does not achieve sub-shot-noise precision. Our demonstration implies improved performance of spin squeezing for applications to quantum metrology.

arXiv:1610.03790•New Journal of Physics•May 16, 2017•6 citations

Sub-Shot Noise Interferometry and Quantum Imaging

Richard E. Slusher, Arthur La Porta, Philippe Grangier +2 more

Optimizing the sensitivity for interferometric measurement of optical phase involves maximizing the intensity of the illuminating light source and minimizing any noise sources. Limits to the light source intensity may arise from the availability of a stable high-power laser or from damage to the system being measured. For example, we describe here a scanning confocal polarization microscope designed to image the dynamics of nerve networks. In this case the light intensity limit is set by several factors, including the scanning rate, the required response time and damage limits of the biological system. Assuming a stable experimental configuration for the interferometer and light source, the limiting noise source for visible light interferometry is shot-noise associated with the quantum state of the light inputs to the interferometer. Shot-noise can be thought of as arising from vacuum fluctuations entering the dark input port of the interferometer.(1) These vacuum field fluctuations combine with the light entering the other port to cause shot-noise in the detected photocurrent at the output ports of the interferometer. This shot-noise current normally limits the measured phase variance Δϕ to a value of 1/N where N is the average number of photons detected in a measurement interval. We describe an experiment which demonstrates that this shot-noise limit can be improved by injecting squeezed vacuum into the normally dark input port.(2) In this case the phase variance is reduced below the 1/N limit by the degree of squeezing. In contrast to early experiments,(2) we are now operating the interferometer in a dark fringe mode(3–5) in order to avoid setting a limit to the light level caused by detector saturation (near 1 mW).

Topical Meeting on Quantum-Limited Imaging and Image Processing•Jan 1, 1989•0 citations

Metrology with entangled states

Morgan W. Mitchell

It is well known that classical states of light exhibit shot noise, characteristic of independent or uncorrelated particles. For phase estimation problems, this leads to a shot-noise limited uncertainty of 1/sqrt[N], where N is the number of particles detected. It is also well known that the shot-noise limit is not fundamental: squeezed states and entangled states can be used for sub-shot-noise phase measurements. The uncertainty principle sets a fundamental limit of 1/N, known as the "Heisenberg" limit. We have recently demonstrated a method, using parametric downconversion and post-selection, to generate entangled "NOON" states suitable for sub-shot-noise phase measurements [M.W. Mitchell et al, Nature 429, 161 (2004)]. We generated a three-photon NOON state and demonstrated three-fold improvement in phase resolution with this state. The relationship between phase resolution and phase uncertainty depends on prior information about the phase being estimated. As in the case of phase measurements with squeezed states, extra precision in one dimension is gained at the cost of reduced precision in other dimensions. Only when prior information is incorporated can entangled-state metrology be applied to beat the shot-noise limit. We illustrate this relationship and discuss adaptive strategies for phase estimation and the possibility of reaching the Heisenberg limit.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 18, 2005•17 citations

Control-enhanced quantum metrology under Markovian noise

Yue Zhai, Xiaodong Yang, Kai Tang +5 more

Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises to improve the metrology performance. Our scheme can automatically alter the parameter-encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. By comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in a nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments.

arXiv:2211.01803•Physical Review A•Feb 3, 2023•13 citations
We introduce an optimal metagrating design for position metrology under Poisson shot noise. By using proper electric and magnetic resonances inside the metagrating, the position of the metagrating within an interference field can be extracted with high precision in the presence of shot noise, leading to nearly three orders of magnitude improvement compared to the centroid-fitting-based position metrology with the same number of detected photons. Furthermore, we find that the improvement in precision is closely related to the formation of a phase vortex around the optimal design in the parameter space. The link between the metagrating design, the formation of a phase vortex and the fundamental precision limit using classical light gives new insights to all of these fields.
We introduce an optimal metagrating design for transverse-position metrology in presence of photon shot noise. The proposed working principle is closely related to the formation of a phase vortex in the diffraction orders in the parameter space. Using the topological robustness, we optimize the design and compress all the transverse-position information around a certain point into a small number of detected photons, saturating the shot-noise limit had all the photons used for probing the position been detected. The current scheme avoids the problem of detector saturation in the presence of high probe power while maintaining all the information detected, allowing one to make full use of the high power that is available. Besides, the direct link between the resonant property in the unit cell and the conditions to achieve the bound is given: one with the zeroth dipole resonance and the other one with the anapole condition of the first dipole. The connection between the metagrating design and the optimization using topological robustness along with the fundamental precision limit using classical light gives new insights in all of these fields.
We investigate the optimal strategies for estimating the Mueller matrix with arbitrary numbers of illumination and analysis states, in the presence of signal-independent additive noise or signal-dependent Poisson shot noise. We demonstrate that the architectures that minimize and equalize the estimation variances for both types of noise sources are based on spherical designs of order 2 or 3, and we provide closed-form expressions of the estimation precision obtained with these optimal measurement strategies. The obtained results are important to design Mueller polarimeters in practice and assess their fundamental limits in terms of estimation precision.
Quantum metrology enables estimation of optical phase shifts with precision beyond the shot-noise limit. One way to exceed this limit is to use squeezed states, where the quantum noise of one observable is reduced at the expense of increased quantum noise for its complementary partner. Because shot-noise limits the phase sensitivity of all classical states, reduced noise in the average value for the observable being measured allows for improved phase sensitivity. However, additional phase sensitivity can be achieved using phase estimation strategies that account for the full distribution of measurement outcomes. Here we experimentally investigate a model of optical spin-squeezing, which uses post-selection and photon subtraction from the state generated using a parametric downconversion photon source, and we investigate the phase sensitivity of this model. The Fisher information for all photon-number outcomes shows it is possible to obtain a quantum advantage of 1.58 compared to the shot-noise value for five-photon events, even though due to experimental imperfection, the average noise for the relevant spin-observable does not achieve sub-shot-noise precision. Our demonstration implies improved performance of spin squeezing for applications to quantum metrology.
Optimizing the sensitivity for interferometric measurement of optical phase involves maximizing the intensity of the illuminating light source and minimizing any noise sources. Limits to the light source intensity may arise from the availability of a stable high-power laser or from damage to the system being measured. For example, we describe here a scanning confocal polarization microscope designed to image the dynamics of nerve networks. In this case the light intensity limit is set by several factors, including the scanning rate, the required response time and damage limits of the biological system. Assuming a stable experimental configuration for the interferometer and light source, the limiting noise source for visible light interferometry is shot-noise associated with the quantum state of the light inputs to the interferometer. Shot-noise can be thought of as arising from vacuum fluctuations entering the dark input port of the interferometer.(1) These vacuum field fluctuations combine with the light entering the other port to cause shot-noise in the detected photocurrent at the output ports of the interferometer. This shot-noise current normally limits the measured phase variance Δϕ to a value of 1/N where N is the average number of photons detected in a measurement interval. We describe an experiment which demonstrates that this shot-noise limit can be improved by injecting squeezed vacuum into the normally dark input port.(2) In this case the phase variance is reduced below the 1/N limit by the degree of squeezing. In contrast to early experiments,(2) we are now operating the interferometer in a dark fringe mode(3–5) in order to avoid setting a limit to the light level caused by detector saturation (near 1 mW).
It is well known that classical states of light exhibit shot noise, characteristic of independent or uncorrelated particles. For phase estimation problems, this leads to a shot-noise limited uncertainty of 1/sqrt[N], where N is the number of particles detected. It is also well known that the shot-noise limit is not fundamental: squeezed states and entangled states can be used for sub-shot-noise phase measurements. The uncertainty principle sets a fundamental limit of 1/N, known as the "Heisenberg" limit. We have recently demonstrated a method, using parametric downconversion and post-selection, to generate entangled "NOON" states suitable for sub-shot-noise phase measurements [M.W. Mitchell et al, Nature 429, 161 (2004)]. We generated a three-photon NOON state and demonstrated three-fold improvement in phase resolution with this state. The relationship between phase resolution and phase uncertainty depends on prior information about the phase being estimated. As in the case of phase measurements with squeezed states, extra precision in one dimension is gained at the cost of reduced precision in other dimensions. Only when prior information is incorporated can entangled-state metrology be applied to beat the shot-noise limit. We illustrate this relationship and discuss adaptive strategies for phase estimation and the possibility of reaching the Heisenberg limit.
Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises to improve the metrology performance. Our scheme can automatically alter the parameter-encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. By comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in a nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments.