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Photonics for Quantum (PfQ)

Quantum super-resolution imaging and hypothesis testing

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

Published Jul 19, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2671840

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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.
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.
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.
The direct detection and characterization of exoplanets remains a grand challenge in astrophysics, primarily due to the overwhelming brightness contrast between a host star and its orbiting planets. Coronagraphy and interferometry are established techniques designed to mitigate this stellar glare, but their performance is fundamentally limited by classical noise sources, including shot noise and detector inefficiencies. This paper explores the burgeoning field of quantum-enhanced interferometry as a paradigm-shifting approach to overcome these classical limitations in the context of exoplanet coronagraphy. We review the principles of high-contrast imaging, the fundamental limits of classical interferometry, and introduce how quantum resources, such as entangled photons and quantum non-demolition measurements, can enable sensitivities beyond the standard quantum limit. Specifically, we investigate how quantum correlation techniques and super-resolution concepts can be integrated into advanced coronagraphic and interferometric architectures to significantly improve the signal-to-noise ratio for faint planetary signals. The proposed methodologies aim to leverage quantum metrology principles to reduce noise floors, enhance angular resolution, and suppress unwanted starlight, thereby paving the way for the direct imaging and spectroscopic characterization of Earth-like exoplanets in the habitable zones of distant stars. This theoretical framework provides a roadmap for future experimental endeavors and mission concepts that could unlock unprecedented capabilities in exoplanet research.
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.