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

Physical Review A

Quantum-optimal hypothesis testing for discriminating partially coherent optical sources

Jiandong Zhang, Mei-Ming Zhang, Fan Jia, Chuang Li, Shuai Wang

Published Feb 10, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.111.023706

Related papers

Performance advantage of quantum hypothesis testing for partially coherent optical sources

Jiandong Zhang, Kexin Zhang, Lili Hou +1 more

Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing. The previous studies assume that the potential source is completely incoherent. In this paper, this problem is generalized to the scenario with partially coherent sources and any prior probabilities. We consider quantum-optimal error probability and a classical benchmark of two scenarios depending on the number of available temporal modes M . For M =1, we calculate the quantum Helstrom bound and the error probability of prior-based direct decision. For M ≫1, we analyze the quantum Chernoff bound as well as the Chernoff bound of intensity-based direct imaging. In addition, we propose binary spatial-mode demultiplexing and the result demonstrates asymptotically optimal detection performance. Our findings may shed new light on super-resolution imaging in partially coherent scenarios.

arXiv:2404.18120•Journal of the Optical Society of America B•Sep 24, 2024•1 citation

Performance advantage of discriminating one-versus-two incoherent sources based on quantum hypothesis testing

Jiandong Zhang, Mei-Ming Zhang, Chuang Li +1 more

Detecting the presence of multiple incoherent sources is a fundamental and challenging task for quantum imaging, especially within sub-Rayleigh region. In this paper, the discrimination of one-versus-two point-like incoherent sources in symmetric and asymmetric scenarios is studied. We calculate the quantum lower bounds on error probabilities of making a decision after one-shot and multishot tests. The results are compared with the error probability of prior-based direct guess, and the minimal number of tests required to make a decision outperforming direct guess is discussed. We also show the asymptotic quantum lower bound for a large number of tests. For practical purposes, we propose a specific strategy along with decision rule of which can work without any prior knowledge. With respect to each of two scenarios, the error probability can approach the quantum lower bound in one-shot tests as well as multishot tests. In addition, the potential challenges and solutions in a realistic scenario are analyzed. Our results may contribute to real-world quantum imaging such as microscopy and astronomy.

arXiv:2410.19259•Physical Review A•Nov 4, 2024•1 citation

Optical quantum super-resolution imaging and hypothesis testing

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

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.

arXiv:2202.09406•Nature Communications•Sep 13, 2022•50 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

Passive optical superresolution at the quantum limit

A. I. Lvovsky, Michael R. Grace, Saikat Guha +3 more

For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.

quant-pharXiv:2605.10767•Optica•May 12, 2026•0 citations

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
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.
Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing. The previous studies assume that the potential source is completely incoherent. In this paper, this problem is generalized to the scenario with partially coherent sources and any prior probabilities. We consider quantum-optimal error probability and a classical benchmark of two scenarios depending on the number of available temporal modes M . For M =1, we calculate the quantum Helstrom bound and the error probability of prior-based direct decision. For M ≫1, we analyze the quantum Chernoff bound as well as the Chernoff bound of intensity-based direct imaging. In addition, we propose binary spatial-mode demultiplexing and the result demonstrates asymptotically optimal detection performance. Our findings may shed new light on super-resolution imaging in partially coherent scenarios.
Detecting the presence of multiple incoherent sources is a fundamental and challenging task for quantum imaging, especially within sub-Rayleigh region. In this paper, the discrimination of one-versus-two point-like incoherent sources in symmetric and asymmetric scenarios is studied. We calculate the quantum lower bounds on error probabilities of making a decision after one-shot and multishot tests. The results are compared with the error probability of prior-based direct guess, and the minimal number of tests required to make a decision outperforming direct guess is discussed. We also show the asymptotic quantum lower bound for a large number of tests. For practical purposes, we propose a specific strategy along with decision rule of which can work without any prior knowledge. With respect to each of two scenarios, the error probability can approach the quantum lower bound in one-shot tests as well as multishot tests. In addition, the potential challenges and solutions in a realistic scenario are analyzed. Our results may contribute to real-world quantum imaging such as microscopy and astronomy.
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. 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.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
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.