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:2008.11339 · Physical Review Letters

Quantum Limits of Superresolution in a Noisy Environment

Changhun Oh, Sisi Zhou, Yat Wong, Liang Jiang

Published Mar 26, 2021• 42 citations
arXivHTMLPDF

Abstract

We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with noiseless cases where the quantum Fisher information has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution. In addition, we show that false excitation on an arbitrary measurement, such as dark counts, also makes the classical Fisher information of the measurement approach to zero as the separation goes to zero. Finally, a practically relevant situation resolving two identical thermal sources is quantitatively investigated by using the quantum and classical Fisher information of finite spatial mode multiplexing, showing that the amount of noise poses a limit on the resolution in a noisy system.

DOI
10.1103/physrevlett.126.120502

Related papers

Towards the quantum limit for two bright-source separation estimation

Giacomo Sorelli, Clémentine Rouvière, Ilya Karuseichyk +4 more

Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works, analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, most previous works have either consider low-intensity, or thermal sources. To broaden the applicability of this approach, it is important to extend these results to more general light sources. To this goal, we will present an analytical expression for the Quantum Fisher Information, determining the ultimate resolution limit, for the separation between two sources in an arbitrary Gaussian state. Applying this result to different quantum states, we can shine some light on some relevant questions. We can for example explore the role of partial coherence considering displaced and correlated thermal states, or investigate the importance of quantum correlations by considering squeezed light. In addition to the ultimate quantum limit, we will discuss a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements, which is often sufficient to saturate these limits, and can easily be adapted to incorporate the most common noise sources. Finally, we will present our experimental setup that allows for the generation of the images of two sources with different photon statistics, as well as for spatial mode demultiplexing and we will discuss the first practical implementations if the above mentioned estimation techniques.

SPIE Quantum Technologies•Jun 3, 2022•0 citations

Superresolution imaging of two incoherent optical sources with unequal brightnesses

Jiandong Zhang, Yiwen Fu, Lili Hou +1 more

Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have unequal brightnesses. We give the ultimate precision limit with respect to separation by using the quantum Fisher information. Through the calculation of the classical Fisher information, we analyze and compare several specific measurement schemes including direct measurement, Gaussian mode measurement and zero-photon measurement. The results indicate that Gaussian mode measurement is the nearly optimal for a small separation. On this basis, the effects of relative brightness fluctuation are addressed. Our work provides a positive complement to the aspect of superresolution imaging of incoherent sources.

arXiv:2404.17463•Optics Express•Jun 27, 2024•9 citations

Separation estimation at the quantum limit with arbitrary Gaussian sources

Giacomo Sorelli, Ilya Karuseichyk, Clémentine Rouvière +3 more

Recent works showed that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, so far these results have been either limited to low-intensity, or thermal sources. In this talk, we will present an analytical expression for the Quantum Fisher Information for the separation between two sources in an arbitrary Gaussian states. This expression allows us to determine the ultimate resolution limit for a series of practically relevant states, e.g. correlated or displaced thermal states (corresponding to partially coherent sources) and squeezed states (exhibiting quantum correlations). Moreover, we will show how a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements can be used to saturate these limits. Finally, we will discuss the applicability of the proposed methods in present experimental setups.

Optical and Quantum Sensing and Precision Metrology II•Mar 9, 2022•0 citations

Parameter-Decoupled Quantum Superresolution without Multiparameter Estimation

X. -F. Qian

Quantum superresolution promises to resolve closely spaced sources beyond the diffraction limit, but existing approaches generally rely on idealized source properties or require simultaneous estimation of multiple coupled parameters of realistic sources. Here we introduce a parameter-decoupled measurement that determines the separation of realistic passive sources without estimating their unknown brightness imbalance, mutual coherence, or relative phase. A complete four-parameter quantum Fisher information analysis identifies the separation information that remains accessible in the presence of these nuisance parameters. We then construct a directly measurable log-probability invariant from projection channels whose conditional statistics depend only on the separation. Broad classes of channel pairs satisfy the resulting decoupling condition. For a Gaussian point-spread function, the lowest-order implementation asymptotically attains the four-parameter quantum limit per incident signal in the sub-Rayleigh regime. This approach converts a realistic multiparameter imaging problem into an operationally single-parameter measurement, providing a practical route toward quantum-enhanced resolution of passive spatial, temporal, and spectral signals.

quant-pharXiv:2609.21796•Sep 21, 2026•0 citations

Moment-based superresolution: Formalism and applications

Giacomo Sorelli, Manuel Gessner, Mattia Walschaers +1 more

Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently, this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits usually require the full measurement statistics, which can be challenging to access. In this work we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial-mode demultiplexing. For demultiplexing, our method is optimal, i.e., it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity, and the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise.

arXiv:2105.12396•Physical Review A•Sep 15, 2021•28 citations

Superresolution picks entanglement over coherence

Abdelali Sajia, X. -F. Qian

Fundamental wave features of light play an important role in the realization of superresolution for two spatially separated point sources. It has been shown that (partial) coherence, which is an inevitable feature in practical light propagation, is harmful to measurement precision thus preventing superresolution. Here we study the quantitative effect of another fundamental feature, entanglement, on the quality of superresolution and compare it with that of coherence. Both single- and two-parameter estimations are analyzed in detail. Surprisingly, contrary to coherence, it is found that superresolution measurement precision (in terms of Fisher Information) can be enhanced as the amount of entanglement increases. More importantly, our analysis shows that non-zero entanglement always guarantees the non-vanishing of Fisher Information. Thus, while coherence is unwanted, entanglement is a favorable feature for superresolution.

arXiv:2302.04909•Feb 9, 2023•0 citations
We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with noiseless cases where the quantum Fisher information has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution. In addition, we show that false excitation on an arbitrary measurement, such as dark counts, also makes the classical Fisher information of the measurement approach to zero as the separation goes to zero. Finally, a practically relevant situation resolving two identical thermal sources is quantitatively investigated by using the quantum and classical Fisher information of finite spatial mode multiplexing, showing that the amount of noise poses a limit on the resolution in a noisy system.
Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works, analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, most previous works have either consider low-intensity, or thermal sources. To broaden the applicability of this approach, it is important to extend these results to more general light sources. To this goal, we will present an analytical expression for the Quantum Fisher Information, determining the ultimate resolution limit, for the separation between two sources in an arbitrary Gaussian state. Applying this result to different quantum states, we can shine some light on some relevant questions. We can for example explore the role of partial coherence considering displaced and correlated thermal states, or investigate the importance of quantum correlations by considering squeezed light. In addition to the ultimate quantum limit, we will discuss a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements, which is often sufficient to saturate these limits, and can easily be adapted to incorporate the most common noise sources. Finally, we will present our experimental setup that allows for the generation of the images of two sources with different photon statistics, as well as for spatial mode demultiplexing and we will discuss the first practical implementations if the above mentioned estimation techniques.
Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have unequal brightnesses. We give the ultimate precision limit with respect to separation by using the quantum Fisher information. Through the calculation of the classical Fisher information, we analyze and compare several specific measurement schemes including direct measurement, Gaussian mode measurement and zero-photon measurement. The results indicate that Gaussian mode measurement is the nearly optimal for a small separation. On this basis, the effects of relative brightness fluctuation are addressed. Our work provides a positive complement to the aspect of superresolution imaging of incoherent sources.
Recent works showed that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, so far these results have been either limited to low-intensity, or thermal sources. In this talk, we will present an analytical expression for the Quantum Fisher Information for the separation between two sources in an arbitrary Gaussian states. This expression allows us to determine the ultimate resolution limit for a series of practically relevant states, e.g. correlated or displaced thermal states (corresponding to partially coherent sources) and squeezed states (exhibiting quantum correlations). Moreover, we will show how a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements can be used to saturate these limits. Finally, we will discuss the applicability of the proposed methods in present experimental setups.
Quantum superresolution promises to resolve closely spaced sources beyond the diffraction limit, but existing approaches generally rely on idealized source properties or require simultaneous estimation of multiple coupled parameters of realistic sources. Here we introduce a parameter-decoupled measurement that determines the separation of realistic passive sources without estimating their unknown brightness imbalance, mutual coherence, or relative phase. A complete four-parameter quantum Fisher information analysis identifies the separation information that remains accessible in the presence of these nuisance parameters. We then construct a directly measurable log-probability invariant from projection channels whose conditional statistics depend only on the separation. Broad classes of channel pairs satisfy the resulting decoupling condition. For a Gaussian point-spread function, the lowest-order implementation asymptotically attains the four-parameter quantum limit per incident signal in the sub-Rayleigh regime. This approach converts a realistic multiparameter imaging problem into an operationally single-parameter measurement, providing a practical route toward quantum-enhanced resolution of passive spatial, temporal, and spectral signals.
Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently, this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits usually require the full measurement statistics, which can be challenging to access. In this work we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial-mode demultiplexing. For demultiplexing, our method is optimal, i.e., it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity, and the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise.
Fundamental wave features of light play an important role in the realization of superresolution for two spatially separated point sources. It has been shown that (partial) coherence, which is an inevitable feature in practical light propagation, is harmful to measurement precision thus preventing superresolution. Here we study the quantitative effect of another fundamental feature, entanglement, on the quality of superresolution and compare it with that of coherence. Both single- and two-parameter estimations are analyzed in detail. Surprisingly, contrary to coherence, it is found that superresolution measurement precision (in terms of Fisher Information) can be enhanced as the amount of entanglement increases. More importantly, our analysis shows that non-zero entanglement always guarantees the non-vanishing of Fisher Information. Thus, while coherence is unwanted, entanglement is a favorable feature for superresolution.