Quantum-inspired exoplanet detection in the presence of experimental imperfections

TL;DR

This work reframes exoplanet detection as asymmetric hypothesis testing and analyzes SPADE under realistic noise sources, notably crosstalk and dark counts. It derives an explicit noisy-SPADE decision rule and shows the asymptotic miss-probability decay $\beta(N) \approx \exp[-ND(\text{H0}|\text{H1})]$ with the practical relative entropy $D_{SD} \approx p_s - p_0\left(1 + \ln\frac{p_s}{p_0}\right)$, where $p_s \approx p_{cross}+p_{dark}+\nu s^2$ and $p_0 \approx p_{cross}+p_{dark}$. Compared to direct imaging and coronagraphs, noisy SPADE retains a favorable scaling in the sub-Rayleigh regime and can offer orders-of-magnitude improvements in required sample size for target miss probabilities, provided noise is kept manageable. The paper also presents a binary-SPADE decision rule, a 51 Pegasi b–like exoplanet example demonstrating feasible detection times within tens of parsecs, and outlines practical paths for noise mitigation and future extensions to multi-source and dynamic scenarios.

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.

Figures (4)

• Figure 1: Schematic representation of the considered measurement scenario. Under hypothesis H0, there is only one source. Under hypothesis H1, there are two sources separated by distance $d$ and characterized by relative brightness $\nu$, with the same total brightness as the source from hypothesis H0. In both hypotheses, the coordinate system is aligned with the system's center of brightness. The SPADE measurement is vulnerable to two forms of experimental noise: crosstalk, i.e., the possibility of measuring a photon in the incorrect mode, and dark counts, i.e., the possibility of measuring a photon not originating from the studied system.
• Figure 2: Comparison of relative entropies $D$ as a function of relative brightness-rescaled separation $\sqrt{\nu}s$. The top black and bottom red dashed curves correspond to the quantum bound (\ref{['eq:D_Q']}) and ideal direct imaging (\ref{['eq:D_DI']}), respectively. The green band corresponds to noisy SPADE (\ref{['eq:D_SPADE_general']}) with noise strength varying from low, $p_0=10^{-4}$, up to large, $p_0=0.02$. For realistic noise strengths, the scaling of SPADE is the same as for direct imaging, albeit with a much larger scaling coefficient, here resulting in from one up to four orders of magnitude of advantage in the value of the relative entropy. Through Eq. (\ref{['eq:beta_asymptotic_decay']}), this translates to several orders of magnitude of advantage in the required sample size $N$ for a fixed target miss probability. For reference, the blue solid line shows how SPADE scales for the very low noise strength $p_0=10^{-6}$, illustrating the dual behavior (\ref{['eq:D_SPADE_regimes']}).
• Figure 3: Top: Detection probability $P_{\textnormal{det}}$ as a function of sample size $N$ for the typical threshold false alarm probability $\bar{\alpha}=0.05$ and relative brightness $\nu=10^{-5}$ (corresponding to Hot Jupiters coronagraphs_perfect_Deshler_experiment_2024). Solid (dashed) curves were drawn assuming large noise strength, $p_0=0.02$ (small noise strength, $p_0=10^{-4}$) unbalanced_sources_crosstalk_Linowski_2023hypothesis_testing_Schlichtholz_2024 and correspond to different separations: $s=\{0.16,0.06,0.02\}$ (left to right) crosstalk_original_PRLBoucher:20unbalanced_sources_crosstalk_Linowski_2023hypothesis_testing_Schlichtholz_2024. Bottom: Detection probability $P_{\textnormal{det}}$ as a function of threshold false alarm probability $\bar{\alpha}$ for sample size $N=2\cdot 10^{13}$ (the same order of magnitude as in the proof of principle experiment SPADE_superresolution_experiment_Rouviere_2024), relative brightness $\nu=10^{-5}$ and separation $s=0.06$. From top to bottom, the curves correspond to noise strengths $p_0=\{0.0001,0.003,0.006,0.01,0.02\}$.
• Figure 4: Detection time $t$ as a function of distance $d_{\textnormal{sys}}$ of the telescope from 51 Pegasi-like system with Hot Jupiter-like exoplanet (for 51 Pegasi itself, $d_{\textnormal{sys}}\approx 15$ pc). The two sets of curves, dashed and solid, correspond to large and small noise strengths, $p_0=10^{-2}$ and $p_0=10^{-4}$, respectively. Within each set, the different curves correspond to different target detection probabilities, from top to bottom: $P_\textnormal{det}=\{0.9999,\,0.999,\,0.99,\,0.9\}$ (magenta, blue, green, red). The threshold false alarm probability was set to $\bar{\alpha}=0.05$ in all the plots. As seen, the plotted detection times remain feasible in the considered parameter ranges.