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:2202.09406 · Nature Communications

Optical quantum super-resolution imaging and hypothesis testing

Ugo Zanforlin, Cosmo Lupo, Peter W. R. Connolly, Pieter Kok, Gerald S. Buller, Zixin Huang

Published Sep 13, 2022• 50 citations
arXivHTMLPDF

Abstract

Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially at lengths within the diffraction limit. Moreover, detecting the presence of multiple sources of different brightness is an even more severe challenge. We experimentally demonstrate two tasks for super-resolution imaging based on hypothesis testing and quantum metrology techniques. We can significantly reduce the error probability for detecting a weak secondary source, even for small separations. We reduce the experimental complexity to a simple interferometer: we show (1) our set-up is optimal for the state discrimination task, and (2) if the two sources are equally bright, then this measurement can super-resolve their angular separation. Using a collection baseline of 5.3 mm, we resolve the angular separation of two sources placed 15 μm apart at a distance of 1.0 m with a 1.7% accuracy - an almost 3-orders-of-magnitude improvement over shot-noise limited direct imaging.

DOI
10.1038/s41467-022-32977-8

Related papers

Quantum super-resolution imaging and hypothesis testing

Ugo Zanforlin, Cosmo Lupo, Peter W. R. Connolly +3 more

Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Estimating the angular separation between two incoherent thermal sources is a also challenging task for direct imaging. Here, we experimentally demonstrate two tasks for super-resolution imaging based on hypothesis testing, quantum state discrimination and quantum imaging techniques. We show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source (e.g. a planet), especially when the two sources have small angular separations. We reduce the experimental complexity down to a single two-input interferometer: we show that (1) this simple set-up is sufficient for the state discrimination task, and (2) if the two sources are of equal brightness, then this measurement can super-resolve their angular separation, saturating the quantum Cramér-Rao bound. By using a collection baseline of 5.3 mm, we resolve the angular separation of two sources that are placed 15 m apart at a distance of 1.0 μm with an accuracy of 1:7% { this is between 2 to 3 orders of magnitudes more accurate than shot-noise limited direct imaging.

Photonics for Quantum (PfQ)•Jul 19, 2023•0 citations

Quantum Hypothesis Testing for Exoplanet Detection

Zixin Huang, Cosmo Lupo

Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging techniques, we show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source, especially when the two sources have small angular separations. If the weak source has intensity ε≪1 relative to the bright source, we find that the error exponent can be improved by a factor of 1/ε. We also find linear-optical measurements that are optimal in this regime. Our result serves as a complementary method in the toolbox of optical imaging, with applications ranging from astronomy to microscopy.

arXiv:2106.00488•Physical Review Letters•Sep 23, 2021•54 citations

Quantum hypothesis testing for exoplanet detection and spectroscopy

Zixin Huang, Cosmo Lupo

Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging techniques, we show that one can significantly reduce the probability of error in detecting the presence of a weak secondary source, even when the two sources have small angular separations. Similar techniques can be applied to perform atmospheric spectroscopy.

Quantum 2.0 Conference and Exhibition•Jan 1, 2023•0 citations

Quantum-optimal hypothesis testing for discriminating partially coherent optical sources

Jiandong Zhang, Mei-Ming Zhang, Fan Jia +2 more

Discriminating a weak optical source that may be hidden near a known optical source is a fundamental and challenging task for quantum imaging, especially for small spatial separations. Previous works in this regard focused on two incoherent sources. Here, we complement this subject by extending the application scenario to two partially coherent sources. The lower limit on the error probability is investigated through analytical calculation of the quantum Bhattacharyya bound. We present two quantum-optimal detection strategies of which error probabilities decided by likelihood ratio test can approach the quantum Bhattacharyya bound. For practical purposes, we propose a simplified decision rule for these two strategies, which can greatly reduce the complexity of the discrimination task. In addition, the effects originating from spatial coherence and relative brightness are discussed. Our work provides insights into quantum imaging and opens a promising avenue for real-world imaging.

Physical Review A•Feb 10, 2025•0 citations

Multiparameter approach to experimental separation estimation of unequally bright sources

Antonin Grateau, Alexander Boeschoten, Tanguy Favin-Lévêque +1 more

Due to the wave nature of light, optical imaging is inherently subject to diffraction, which typically dictates the resolution limit for two-point sources. A practical way to describe this phenomenon is through Rayleigh’s criterion, which states that two sources are barely resolvable when the minimum of one source's diffraction pattern coincides with the maximum of the other. However, recent advances in optical quantum metrology have shown that this classical limit can be surpassed by leveraging the spatial correlations within the light field. Specifically, decomposing the light into a Hermite-Gauss mode basis provides substantially more information than traditional direct imaging, which measures local intensity [1,2,3]. In this work, we implement a spatial demultiplexing technique to estimate the separation between light sources of unequal brightness. This unknown imbalance adds complexity to the estimation task, making it inherently a multiparameter problem and thus requiring a multimode approach [4]. By optimizing the measurement strategy and introducing a shift between two demultiplexers, we achieve sub-Rayleigh resolution in distance measurements without assuming prior knowledge of the intensity imbalance or alignment. [1] Tsang, M., Nair, R., & Lu, X. M. (2016). Quantum theory of superresolution for two incoherent optical point sources. Physical Review X, 6(3), 031033. [2] Sorelli, G., Gessner, M., Walschaers, M., & Treps, N. (2021). Optimal observables and estimators for practical superresolution imaging. Physical Review Letters, 127(12), 123604. [3] Rouvière, C., Barral, D., Grateau, A., Karuseichyk, I., Sorelli, G., Walschaers, M., & Treps, N. (2024). Ultra-sensitive separation estimation of optical sources. Optica, 11(2), 166-170. [4] Řeháček, J., Hradil, Z., Koutný, D., Grover, J., Krzic, A., & Sánchez-Soto, L. L. (2018). Optimal measurements for quantum spatial superresolution. Physical review A, 98(1), 012103.

SPIE Quantum Technologies for Defence and Security•Oct 29, 2025•0 citations

Quantum-optimal detection of one-versus-two incoherent optical sources with arbitrary separation

Xiao-Ming Lu, Hari Krovi, Ranjith Nair +2 more

Abstract We analyze the fundamental quantum limit of the resolution of an optical imaging system from the perspective of the detection problem of deciding whether the optical field in the image plane is generated by one incoherent on-axis source with brightness $$\epsilon$$ ϵ or by two $$\epsilon {\mathrm{/}}2$$ ϵ ∕ 2 -brightness incoherent sources that are symmetrically disposed about the optical axis. Using the exact thermal-state model of the field, we derive the quantum Chernoff bound for the detection problem, which specifies the optimum rate of decay of the error probability with increasing number of collected photons that is allowed by quantum mechanics. We then show that recently proposed linear-optic schemes approach the quantum Chernoff bound—the method of binary spatial-mode demultiplexing (B-SPADE) is quantum-optimal for all values of separation, while a method using image inversion interferometry (SLIVER) is near-optimal for sub-Rayleigh separations. We then simplify our model using a low-brightness approximation that is very accurate for optical microscopy and astronomy, derive quantum Chernoff bounds conditional on the number of photons detected, and show the optimality of our schemes in this conditional detection paradigm. For comparison, we analytically demonstrate the superior scaling of the Chernoff bound for our schemes with source separation relative to that of spatially resolved direct imaging. Our schemes have the advantages over the quantum-optimal (Helstrom) measurement in that they do not involve joint measurements over multiple modes, and that they do not require the angular separation for the two-source hypothesis to be given a priori and can offer that information as a bonus in the event of a successful detection.

arXiv:1609.03025•npj Quantum Information•Dec 3, 2018•67 citations
Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially at lengths within the diffraction limit. Moreover, detecting the presence of multiple sources of different brightness is an even more severe challenge. We experimentally demonstrate two tasks for super-resolution imaging based on hypothesis testing and quantum metrology techniques. We can significantly reduce the error probability for detecting a weak secondary source, even for small separations. We reduce the experimental complexity to a simple interferometer: we show (1) our set-up is optimal for the state discrimination task, and (2) if the two sources are equally bright, then this measurement can super-resolve their angular separation. Using a collection baseline of 5.3 mm, we resolve the angular separation of two sources placed 15 μm apart at a distance of 1.0 m with a 1.7% accuracy - an almost 3-orders-of-magnitude improvement over shot-noise limited direct imaging.
Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Estimating the angular separation between two incoherent thermal sources is a also challenging task for direct imaging. Here, we experimentally demonstrate two tasks for super-resolution imaging based on hypothesis testing, quantum state discrimination and quantum imaging techniques. We show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source (e.g. a planet), especially when the two sources have small angular separations. We reduce the experimental complexity down to a single two-input interferometer: we show that (1) this simple set-up is sufficient for the state discrimination task, and (2) if the two sources are of equal brightness, then this measurement can super-resolve their angular separation, saturating the quantum Cramér-Rao bound. By using a collection baseline of 5.3 mm, we resolve the angular separation of two sources that are placed 15 m apart at a distance of 1.0 μm with an accuracy of 1:7% { this is between 2 to 3 orders of magnitudes more accurate than shot-noise limited direct imaging.
Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging techniques, we show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source, especially when the two sources have small angular separations. If the weak source has intensity ε≪1 relative to the bright source, we find that the error exponent can be improved by a factor of 1/ε. We also find linear-optical measurements that are optimal in this regime. Our result serves as a complementary method in the toolbox of optical imaging, with applications ranging from astronomy to microscopy.
Discriminating a weak optical source that may be hidden near a known optical source is a fundamental and challenging task for quantum imaging, especially for small spatial separations. Previous works in this regard focused on two incoherent sources. Here, we complement this subject by extending the application scenario to two partially coherent sources. The lower limit on the error probability is investigated through analytical calculation of the quantum Bhattacharyya bound. We present two quantum-optimal detection strategies of which error probabilities decided by likelihood ratio test can approach the quantum Bhattacharyya bound. For practical purposes, we propose a simplified decision rule for these two strategies, which can greatly reduce the complexity of the discrimination task. In addition, the effects originating from spatial coherence and relative brightness are discussed. Our work provides insights into quantum imaging and opens a promising avenue for real-world imaging.
Due to the wave nature of light, optical imaging is inherently subject to diffraction, which typically dictates the resolution limit for two-point sources. A practical way to describe this phenomenon is through Rayleigh’s criterion, which states that two sources are barely resolvable when the minimum of one source's diffraction pattern coincides with the maximum of the other. However, recent advances in optical quantum metrology have shown that this classical limit can be surpassed by leveraging the spatial correlations within the light field. Specifically, decomposing the light into a Hermite-Gauss mode basis provides substantially more information than traditional direct imaging, which measures local intensity [1,2,3]. In this work, we implement a spatial demultiplexing technique to estimate the separation between light sources of unequal brightness. This unknown imbalance adds complexity to the estimation task, making it inherently a multiparameter problem and thus requiring a multimode approach [4]. By optimizing the measurement strategy and introducing a shift between two demultiplexers, we achieve sub-Rayleigh resolution in distance measurements without assuming prior knowledge of the intensity imbalance or alignment. [1] Tsang, M., Nair, R., & Lu, X. M. (2016). Quantum theory of superresolution for two incoherent optical point sources. Physical Review X, 6(3), 031033. [2] Sorelli, G., Gessner, M., Walschaers, M., & Treps, N. (2021). Optimal observables and estimators for practical superresolution imaging. Physical Review Letters, 127(12), 123604. [3] Rouvière, C., Barral, D., Grateau, A., Karuseichyk, I., Sorelli, G., Walschaers, M., & Treps, N. (2024). Ultra-sensitive separation estimation of optical sources. Optica, 11(2), 166-170. [4] Řeháček, J., Hradil, Z., Koutný, D., Grover, J., Krzic, A., & Sánchez-Soto, L. L. (2018). Optimal measurements for quantum spatial superresolution. Physical review A, 98(1), 012103.
Abstract We analyze the fundamental quantum limit of the resolution of an optical imaging system from the perspective of the detection problem of deciding whether the optical field in the image plane is generated by one incoherent on-axis source with brightness ϵ\epsilonϵ ϵ or by two ϵ/2\epsilon {\mathrm{/}}2ϵ/2 ϵ ∕ 2 -brightness incoherent sources that are symmetrically disposed about the optical axis. Using the exact thermal-state model of the field, we derive the quantum Chernoff bound for the detection problem, which specifies the optimum rate of decay of the error probability with increasing number of collected photons that is allowed by quantum mechanics. We then show that recently proposed linear-optic schemes approach the quantum Chernoff bound—the method of binary spatial-mode demultiplexing (B-SPADE) is quantum-optimal for all values of separation, while a method using image inversion interferometry (SLIVER) is near-optimal for sub-Rayleigh separations. We then simplify our model using a low-brightness approximation that is very accurate for optical microscopy and astronomy, derive quantum Chernoff bounds conditional on the number of photons detected, and show the optimality of our schemes in this conditional detection paradigm. For comparison, we analytically demonstrate the superior scaling of the Chernoff bound for our schemes with source separation relative to that of spatially resolved direct imaging. Our schemes have the advantages over the quantum-optimal (Helstrom) measurement in that they do not involve joint measurements over multiple modes, and that they do not require the angular separation for the two-source hypothesis to be given a priori and can offer that information as a bonus in the event of a successful detection.