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arXiv:2403.17988 · Physical Review A

Quantum limits of exoplanet detection and localization

Nico Deshler, Sebastiaan Y. Haffert, Amit Ashok

Published Nov 11, 2025• 3 citations
arXivHTMLPDF

Abstract

Discovering exoplanets in orbit around distant stars via direct imaging is fundamentally impeded by the combined effect of optical diffraction and photon shot noise under extreme star-planet contrast. Coronagraphs strive to increase the signal-to-noise ratio of exoplanet signatures by optically suppressing light from the host star while preserving light from the exoplanet. However, it is unclear whether direct-imaging coronagraphs constitute an optimal strategy for attaining fundamental limits relevant to exoplanet discovery. In this work, we first review the quantum information limits of exoplanet detection and localization characterized by (1) the quantum Chernoff exponent for symmetric hypothesis testing, (2) the quantum relative entropy for asymmetric hypothesis testing, and (3) the quantum Fisher information matrix for multiparameter estimation. We demonstrate that coronagraphs designed to completely suppress light in the fundamental mode of the telescope, while perfectly transmitting higher-order orthogonal modes, indeed achieve these limits in the regime of high star-planet contrasts. Furthermore, we formulate coronagraphs as quantum channels, thus generalizing the classical framework of coronagraphy to the quantum setting. Using this framework, we compare the information-theoretic performance of leading coronagraph designs against the quantum limits. Our analysis indicates that quantum-optimal coronagraphs offer enhanced information efficiency in the subdiffraction regime compared to leading coronagraph designs and may significantly expand the domain of accessible exoplanets.

DOI
10.1103/g6kr-mqdj

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Discovering exoplanets in orbit around distant stars via direct imaging is fundamentally impeded by the combined effect of optical diffraction and photon shot noise under extreme star-planet contrast. Coronagraphs strive to increase the signal-to-noise ratio of exoplanet signatures by optically suppressing light from the host star while preserving light from the exoplanet. However, it is unclear whether direct-imaging coronagraphs constitute an optimal strategy for attaining fundamental limits relevant to exoplanet discovery. In this work, we first review the quantum information limits of exoplanet detection and localization characterized by (1) the quantum Chernoff exponent for symmetric hypothesis testing, (2) the quantum relative entropy for asymmetric hypothesis testing, and (3) the quantum Fisher information matrix for multiparameter estimation. We demonstrate that coronagraphs designed to completely suppress light in the fundamental mode of the telescope, while perfectly transmitting higher-order orthogonal modes, indeed achieve these limits in the regime of high star-planet contrasts. Furthermore, we formulate coronagraphs as quantum channels, thus generalizing the classical framework of coronagraphy to the quantum setting. Using this framework, we compare the information-theoretic performance of leading coronagraph designs against the quantum limits. Our analysis indicates that quantum-optimal coronagraphs offer enhanced information efficiency in the subdiffraction regime compared to leading coronagraph designs and may significantly expand the domain of accessible exoplanets.
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 terrestrial exoplanets in the habitable zones of nearby stars remains a critical challenge. Such planets can be 10810^8108 to 101010^{10}1010 times fainter than their host stars and lie at diffraction-limited angular separations, where starlight strongly obscures the companion signal. Here we present an adaptive quantum measurement method for estimating the number, positions, and brightnesses of mutually incoherent point sources in the sub-Rayleigh, ultra-high-contrast regime, operating at contrasts down to 10−810^{-8}10−8 -- five orders of magnitude beyond previous quantum imaging approaches to exoplanet detection. The method adopts a spatial-mode basis that is updated to maximize the quantum Fisher information per detected photon. Estimation is performed by maximum likelihood in log-brightness coordinates, and the source count is determined by Bayesian-information-criterion (BIC) model selection directly from photon-count statistics, without a tunable detection threshold. For point sources within sub-Rayleigh separations and with brightness ratios spanning eight orders of magnitude, the method reconstructs complete scenes with a mean success rate of 72.5%72.5\%72.5%. Furthermore, it is robust to misalignment, maintaining a 71.3%71.3\%71.3% success rate under offsets of up to six pixels. These results demonstrate that terrestrial exoplanets can be detected below the Rayleigh limit, a regime previously inaccessible to direct imaging.
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.
One of the big challenges in exoplanet science is to determine the atmospheric makeup of extrasolar planets and to find biosignatures that hint at the existence of biochemical processes on another world. The biomarkers we are trying to detect are gases in the exoplanet atmosphere such as oxygen or methane, which have deep absorption features in the visible and near-infrared spectrum. Here we establish the ultimate quantum limit for determining the presence or absence of a spectral absorption line, for a dim source in the presence of a much brighter stellar source. We characterize the associated error exponent in both the frameworks of symmetric and asymmetric hypothesis testing. We found that a structured measurement based on spatial demultiplexing allows us to decouple the light coming from the planet and achieve the ultimate quantum limits. If the planet has intensity $\ensuremath{\epsilon}\ensuremath{\ll}1$ relative to the star, we show that this approach significantly outperforms direct spectroscopy yielding an improvement of the error exponent by a factor $1/\ensuremath{\epsilon}$. We find the optimal measurement, which is a combination of interferometric techniques and spectrum analysis.
Recent advances in quantum information theory have led to the development of quantum imaging methods that would allow optical interferometers to achieve resolutions surpassing the conventional diffraction limit. The use of quantum technologies also has the potential to create optical interferometer telescopes with baselines of hundreds of kilometers, achieving unprecedented imaging resolution. We present results of laboratory experiments advancing quantum interferometer techniques for astronomy. We demonstrate quantum-optimal imaging of an artificial star-like source using a phase-stabilized 170 km-span optical interferometer, pointing the way to astronomical interferometers with resolution orders of magnitude better than any current telescope, with outstanding applications for studying exoplanets, the formation of star systems, and tests of General Relativity near the event horizon of a black hole.
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.