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arXiv:2505.00064 · Physical Review Applied

Quantum-inspired exoplanet detection in the presence of experimental imperfections

Tomasz Linowski, Konrad Schlichtholz, Giacomo Sorelli

Published Sep 24, 2025• 2 citations
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Abstract

Ideal spatial demultiplexing (SPADE) is proven to be a quantum-optimal tool for exoplanet detection, i.e., asymmetric source discrimination. However, recent investigations into the related problems of separation estimation and symmetric source discrimination showed its efficiency to be limited in the presence of noise. In this work, we use analytical tools to scrutinize the practical applicability of SPADE and derive the associated optimal decision strategy for exoplanet detection in the presence of experimental imperfections. On the one hand, we find that the probability of detection of noisy SPADE has the same scaling with planet-star separation and relative brightness as conventional techniques, such as direct imaging and coronagraphs. On the other hand, we prove that, due to a superior scaling coefficient under realistic noise conditions, SPADE remains the most efficient method for practical exoplanet detection in the sub-Rayleigh regime.

DOI
10.1103/qq99-jmpv

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Ideal spatial demultiplexing (SPADE) is proven to be a quantum-optimal tool for exoplanet detection, i.e., asymmetric source discrimination. However, recent investigations into the related problems of separation estimation and symmetric source discrimination showed its efficiency to be limited in the presence of noise. In this work, we use analytical tools to scrutinize the practical applicability of SPADE and derive the associated optimal decision strategy for exoplanet detection in the presence of experimental imperfections. On the one hand, we find that the probability of detection of noisy SPADE has the same scaling with planet-star separation and relative brightness as conventional techniques, such as direct imaging and coronagraphs. On the other hand, we prove that, due to a superior scaling coefficient under realistic noise conditions, SPADE remains the most efficient method for practical exoplanet detection in the sub-Rayleigh regime.
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.
We propose a Bayesian evidence-based inference framework based on relative belief ratios and apply it to discriminating between one and two incoherent optical point sources using spatial-mode demultiplexing (SPADE). Unlike the Helstrom measurement, SPADE require no collective detection and its optimal for asymptotically large samples. Our method avoids ad hoc statistical constructs and relies solely on the information contained in the data, with all assumptions entering only through the likelihood model and prior beliefs. Using experimental evidence, we demonstrate the superior resolving performance of SPADE over direct imaging from a new and extensible perspective; one that naturally generalizes to multiple sources and offers a practical robust approach to analyzing quantum-enhanced superresolution.
We experimentally demonstrate a universal, parameter-independent test for asymmetric source discrimination below the diffraction limit. The test exploits spatial-mode demultiplexing (SPADE) and single-photon detection to discriminate the presence of a faint source in the vicinity of a brighter one. We develop a complete theory of the test in the presence of arbitrary modal crosstalk and show that the crosstalk-affected test retains a favorable error exponent over diffraction-limited direct imaging, provided that the crosstalk remains below a threshold Cmax≃1/9C_{\mathrm{max}}\simeq 1/9Cmax​≃1/9. This establishes a quantitative condition under which the subdiffraction advantage of SPADE survives realistic imperfections. We experimentally test the scheme for a range of source separations and intensity ratios, without requiring prior knowledge of these parameters. The measured false-negative error rates are in good agreement with the theoretical model and systematically outperform direct imaging. These results demonstrate that SPADE provides a robust and experimentally accessible advantage for asymmetric subdiffraction hypothesis testing in the photon-starved regime, even in the presence of realistic modal crosstalk.
Interferometric methods have been recently investigated to achieve sub-Rayleigh imaging and precision measurements of faint incoherent sources up to the ultimate quantum limit. Here we consider single-photon imaging of two point-like emitters of unequal intensity. This is motivated by the fact that pairs of natural emitters typically have unequal brightness, for example, binary star systems and exoplanets. We address the problem of estimating the transverse separation d or the relative intensity . Our theoretical analysis shows that the associated statistical errors are qualitatively different from the case of equal intensity. We employ multi-plane light conversion technology to implement Hermite–Gaussian (HG) spatial-mode demultiplexing (SPADE), and demonstrate sub-Rayleigh measurement of two emitters with a Gaussian point-spread function. The experimental errors are comparable with the theoretical bounds. The latter are benchmarked against direct imaging, yielding an improvement in the signal-to-noise ratio, which may be significant when the primary source is much brighter than the secondary one, for example, as for imaging of exoplanets.
We theoretically predict and experimentally demonstrate that a reduced spatial-mode demultiplexing (SPADE) measurement using only the two lowest-order Hermite-Gaussian modes exhibits remarkable robustness against background noise in discriminating between a single source and two incoherent point sources. We establish a theoretical framework incorporating uniform background noise and derive an analytical Chernoff exponent expression, showing that SPADE consistently outperforms direct imaging (DI) across all source separations. Experimental results confirm that SPADE-based hypothesis testing approaches the quantum limit even when the background-to-signal photon ratio per pixel is 0.11. This advantage stems from SPADE's ability to concentrate source information into minimal detection modes, reducing the cumulative background noise impact. Our findings provide a practical detection scheme for applications where background noise is inevitable, such as astronomical observations and quantum sensing.
Superresolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk [Phys. Rev. Lett. 125, 100501 (2020)]. In this work, we consider arbitrarily unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE. As we dissect, in this generalized scenario, SPADE's effectiveness depends non-trivially on the strength of crosstalk, relative brightness and the separation between the sources. In particular, for any source imbalance, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations.