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

arXiv:2308.15024 · Physical Review Letters

Single-Shot Single-Mode Optical Two-Parameter Displacement Estimation beyond Classical Limit

Fumiya Hanamura, Warit Asavanant, Seigo Kikura, Moeto Mishima, Shigehito Miki, Hirotaka Terai, Masahiro Yabuno, Fumihiro China, Kosuke Fukui, Mamoru Endo, Akira Furusawa

Published Dec 7, 2023• 10 citations
arXivHTMLPDF

Abstract

Uncertainty principle prohibits the precise measurement of both components of displacement parameters in phase space. We have theoretically shown that this limit can be beaten using single-photon states, in a single-shot and single-mode setting [F. Hanamura et al., Estimation of gaussian random displacement using non-gaussian states, Phys. Rev. A 104, 062601 (2021).PLRAAN2469-992610.1103/PhysRevA.104.062601]. In this Letter, we validate this by experimentally beating the classical limit. In optics, this is the first experiment to estimate both parameters of displacement using non-Gaussian states. This result is related to many important applications, such as quantum error correction.

DOI
10.1103/physrevlett.131.230801

Related papers

Single-Shot Non-Gaussian Measurements for Optical Phase Estimation

M. T. DiMario, F. E. Becerra

Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the phase of an electromagnetic field and single-shot measurements of this phase are necessary. While there are measurements able to estimate the phase of light in a single shot with small uncertainties, demonstrations of near-optimal single-shot measurements for an unknown phase of a coherent state remain elusive. Here, we propose and demonstrate strategies for single-shot measurements for ab initio phase estimation of coherent states that surpass the sensitivity limit of heterodyne measurement and approach the Cramer-Rao lower bound for coherent states. These single-shot estimation strategies are based on real-time optimization of coherent displacement operations, single photon counting with photon number resolution, and fast feedback. We show that our demonstration of these optimized estimation strategies surpasses the heterodyne limit for a wide range of optical powers without correcting for detection efficiency with a moderate number of adaptive measurement steps. This is, to our knowledge, the most sensitive single-shot measurement of an unknown phase encoded in optical coherent states.

arXiv:2008.08185•Physical Review Letters•Sep 18, 2020•11 citations

Estimation of Gaussian random displacement using non-Gaussian states

Fumiya Hanamura, Warit Asavanant, Kosuke Fukui +2 more

In continuous-variable quantum information processing, quantum error correction of Gaussian errors requires simultaneous estimation of both quadrature components of displacements in phase space. However, quadrature operators $x$ and $p$ are noncommutative conjugate observables, whose simultaneous measurement is prohibited by the uncertainty principle. Gottesman-Kitaev-Preskill (GKP) error correction deals with this problem using complex non-Gaussian states called GKP states. On the other hand, simultaneous estimation of displacement using experimentally feasible non-Gaussian states has not been well studied. In this paper, we consider a multiparameter estimation problem of displacements assuming an isotropic Gaussian prior distribution and allowing postselection of measurement outcomes. We derive a lower bound for the estimation error when only Gaussian operations are used and show that even simple non-Gaussian states such as single-photon states can beat this bound. Based on Ghosh's bound, we also obtain a lower bound for the estimation error when the maximum photon number of the input state is given. Our results reveal the role of non-Gaussianity in the estimation of displacements and pave the way toward the error correction of Gaussian errors using experimentally feasible non-Gaussian states.

arXiv:2102.05276•Physical Review A•Dec 1, 2021•17 citations

Estimation and Correction of Gaussian Random Displacement Error Using Simple Non-Gaussian States

Fumiya Hanamura, Warit Asavanant, Kosuke Fukui +2 more

We analyse estimation and error correction of Gaussian random displacement using experimentally feasible non-Gaussian states. We show that even simple states such as single-photon state is superior to Gaussian states in both settings.

Frontiers in Optics•Jan 1, 2021•0 citations

Optical estimation of unitary Gaussian processes without phase reference using Fock states

Changhun Oh, Ki-min Park B, Radim Filip +2 more

Abstract Since a general Gaussian process is phase-sensitive, a stable phase reference is required to take advantage of this feature. When the reference is missing, either due to the volatile nature of the measured sample or the measurement’s technical limitations, the resulting process appears as random in phase. Under this condition, we consider two single-mode Gaussian processes, displacement and squeezing. We show that these two can be efficiently estimated using photon number states and photon number resolving detectors. For separate estimation of displacement and squeezing, the practical estimation errors for hundreds of probes’ ensembles can saturate the Cramér–Rao bound even for arbitrary small values of the estimated parameters and under realistic losses. The estimation of displacement with Fock states always outperforms estimation using Gaussian states with equivalent energy and optimal measurement. For estimation of squeezing, Fock states outperform Gaussian methods, but only when their energy is large enough. Finally, we show that Fock states can also be used to estimate the displacement and the squeezing simultaneously.

arXiv:2006.09976•New Journal of Physics•Dec 1, 2020•16 citations

Ultimate precision of joint parameter estimation under noisy Gaussian environment

Bakmou Lahcen, Mohammed Daoud A

The major problem of multiparameter quantum estimation theory is to find an ultimate measurement scheme to go beyond the standard quantum limits that each quasi-classical estimation measurement is limited by. Although, in some specifics quantum protocols without environmental noise, the ultimate sensitivity of a multiparameter quantum estimation can beat the standard quantum limit. However, the presence of noise imposes limitations on the enhancement of precision due to the inevitable existence of environmental fluctuations. Here, we address the motivation behind the usage of Gaussian quantum resources and their advantages in reaching the standard quantum limits under realistic noise. In this context, our work aims to explore the ultimate limits of precision for the simultaneous estimation of a pair of parameters that characterize the displacement channel acting on Gaussian probes and subjected to open dynamics. More precisely, we focus on a general two-mode mixed squeezed displaced thermal state, after reducing it to various Gaussian probes states, like; a two-mode pure squeezed vacuum, two-mode pure displaced vacuum, two-mode mixed displaced thermal, two-mode mixed squeezed thermal. To study the ultimate estimation precision, we evaluate the upper and bottom bound of HCRB in various cases. We find that when the entangled states, two-mode pure squeezed vacuum and two-mode mixed squeezed thermal, are employed as probes states, the upper and bottom bound of HCRB beats the standard quantum limit in the presence of a noisy environment.

arXiv:2203.09847•Mar 18, 2022•0 citations

Classical Inputs and Measurements Enable Phase Sensitivity beyond the Shot-Noise Limit

Jiandong Zhang, Zijing Zhang, Longzhu Cen +2 more

Coherent-state-based phase estimation is a fruitful testbed for the field of precision measurements since coherent states are robust to decoherence when compared with exotic quantum states. The seminal work done by Caves (https://doi.org/10.1103/PhysRevD.23.1693 , Phys. Rev. D 23, 1693 (1981)) stated that the phase sensitivity of a U(2) interferometer fed with a coherent state is limited by the shot-noise limit (SNL). In this Letter, we demonstrate that this bound is not conclusive sensitivity limit and can be broken when the measurement includes an external phase reference. The SNL can be surpassed by a factor of $\sqrt{2}$ and the validity is supported through the calculation of quantum Fisher information. Additionally, we discuss other single-mode Gaussian inputs of which sensitivities are beyond the SNL. Our work shows potential applications for many metological scenarios, particularly when the measured samples immersed in great lossy environments or can withstand bright illumination.

arXiv:2001.00160•Jan 1, 2020•1 citation
Uncertainty principle prohibits the precise measurement of both components of displacement parameters in phase space. We have theoretically shown that this limit can be beaten using single-photon states, in a single-shot and single-mode setting [F. Hanamura et al., Estimation of gaussian random displacement using non-gaussian states, Phys. Rev. A 104, 062601 (2021).PLRAAN2469-992610.1103/PhysRevA.104.062601]. In this Letter, we validate this by experimentally beating the classical limit. In optics, this is the first experiment to estimate both parameters of displacement using non-Gaussian states. This result is related to many important applications, such as quantum error correction.
Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the phase of an electromagnetic field and single-shot measurements of this phase are necessary. While there are measurements able to estimate the phase of light in a single shot with small uncertainties, demonstrations of near-optimal single-shot measurements for an unknown phase of a coherent state remain elusive. Here, we propose and demonstrate strategies for single-shot measurements for ab initio phase estimation of coherent states that surpass the sensitivity limit of heterodyne measurement and approach the Cramer-Rao lower bound for coherent states. These single-shot estimation strategies are based on real-time optimization of coherent displacement operations, single photon counting with photon number resolution, and fast feedback. We show that our demonstration of these optimized estimation strategies surpasses the heterodyne limit for a wide range of optical powers without correcting for detection efficiency with a moderate number of adaptive measurement steps. This is, to our knowledge, the most sensitive single-shot measurement of an unknown phase encoded in optical coherent states.
In continuous-variable quantum information processing, quantum error correction of Gaussian errors requires simultaneous estimation of both quadrature components of displacements in phase space. However, quadrature operators xxx and ppp are noncommutative conjugate observables, whose simultaneous measurement is prohibited by the uncertainty principle. Gottesman-Kitaev-Preskill (GKP) error correction deals with this problem using complex non-Gaussian states called GKP states. On the other hand, simultaneous estimation of displacement using experimentally feasible non-Gaussian states has not been well studied. In this paper, we consider a multiparameter estimation problem of displacements assuming an isotropic Gaussian prior distribution and allowing postselection of measurement outcomes. We derive a lower bound for the estimation error when only Gaussian operations are used and show that even simple non-Gaussian states such as single-photon states can beat this bound. Based on Ghosh's bound, we also obtain a lower bound for the estimation error when the maximum photon number of the input state is given. Our results reveal the role of non-Gaussianity in the estimation of displacements and pave the way toward the error correction of Gaussian errors using experimentally feasible non-Gaussian states.
Abstract Since a general Gaussian process is phase-sensitive, a stable phase reference is required to take advantage of this feature. When the reference is missing, either due to the volatile nature of the measured sample or the measurement’s technical limitations, the resulting process appears as random in phase. Under this condition, we consider two single-mode Gaussian processes, displacement and squeezing. We show that these two can be efficiently estimated using photon number states and photon number resolving detectors. For separate estimation of displacement and squeezing, the practical estimation errors for hundreds of probes’ ensembles can saturate the Cramér–Rao bound even for arbitrary small values of the estimated parameters and under realistic losses. The estimation of displacement with Fock states always outperforms estimation using Gaussian states with equivalent energy and optimal measurement. For estimation of squeezing, Fock states outperform Gaussian methods, but only when their energy is large enough. Finally, we show that Fock states can also be used to estimate the displacement and the squeezing simultaneously.
The major problem of multiparameter quantum estimation theory is to find an ultimate measurement scheme to go beyond the standard quantum limits that each quasi-classical estimation measurement is limited by. Although, in some specifics quantum protocols without environmental noise, the ultimate sensitivity of a multiparameter quantum estimation can beat the standard quantum limit. However, the presence of noise imposes limitations on the enhancement of precision due to the inevitable existence of environmental fluctuations. Here, we address the motivation behind the usage of Gaussian quantum resources and their advantages in reaching the standard quantum limits under realistic noise. In this context, our work aims to explore the ultimate limits of precision for the simultaneous estimation of a pair of parameters that characterize the displacement channel acting on Gaussian probes and subjected to open dynamics. More precisely, we focus on a general two-mode mixed squeezed displaced thermal state, after reducing it to various Gaussian probes states, like; a two-mode pure squeezed vacuum, two-mode pure displaced vacuum, two-mode mixed displaced thermal, two-mode mixed squeezed thermal. To study the ultimate estimation precision, we evaluate the upper and bottom bound of HCRB in various cases. We find that when the entangled states, two-mode pure squeezed vacuum and two-mode mixed squeezed thermal, are employed as probes states, the upper and bottom bound of HCRB beats the standard quantum limit in the presence of a noisy environment.
Coherent-state-based phase estimation is a fruitful testbed for the field of precision measurements since coherent states are robust to decoherence when compared with exotic quantum states. The seminal work done by Caves (https://doi.org/10.1103/PhysRevD.23.1693 , Phys. Rev. D 23, 1693 (1981)) stated that the phase sensitivity of a U(2) interferometer fed with a coherent state is limited by the shot-noise limit (SNL). In this Letter, we demonstrate that this bound is not conclusive sensitivity limit and can be broken when the measurement includes an external phase reference. The SNL can be surpassed by a factor of 2\sqrt{2}2​ and the validity is supported through the calculation of quantum Fisher information. Additionally, we discuss other single-mode Gaussian inputs of which sensitivities are beyond the SNL. Our work shows potential applications for many metological scenarios, particularly when the measured samples immersed in great lossy environments or can withstand bright illumination.