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arXiv:2605.05961

Passive Imaging with Quantum Advantage

Li Gong, Aonan Zhang, Madhura Ghosh Dastidar, Alexander Duplinskii, A. I. Lvovsky

quant-phphysics.opticsSubmitted May 7, 2026• Announced May 8, 2026• 0 citations
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Abstract

Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise, particularly the shot noise arising from discrete and random nature of quantum light. Here we propose and implement a method for reducing the effect of this noise by optically pre-processing the incoming light prior to detection, thereby optimizing the quantum measurement performed on it. Our scheme, termed Fourier Domain Division (FDD), partitions the Fourier plane into multiple regions for independent detection and subsequent post-processing for image reconstruction. By analyzing the quantum and classical Fisher information, we show that our method is advantageous with respect to direct imaging for high spatial-frequency components. As a result, the number of photons required to achieve a certain signal-to-noise-ratio in the Fourier domain is reduced, thus enhancing the overall resolution in the photon-starved regime. We demonstrate our method in microscopy, achieving 5-fold improvement of Fisher information on high spatial-frequency components. Unlike active super-resolution methods, FDD is passive, making it broadly applicable in microscopy and other imaging scenarios where active illumination is impractical, including astronomy and remote sensing. Our work establishes a general strategy for designing quantum optimized superresolution imaging systems, bridging fundamental quantum limits, practical image analysis and computer vision applications.

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Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise, particularly the shot noise arising from discrete and random nature of quantum light. Here we propose and implement a method for reducing the effect of this noise by optically pre-processing the incoming light prior to detection, thereby optimizing the quantum measurement performed on it. Our scheme, termed Fourier Domain Division (FDD), partitions the Fourier plane into multiple regions for independent detection and subsequent post-processing for image reconstruction. By analyzing the quantum and classical Fisher information, we show that our method is advantageous with respect to direct imaging for high spatial-frequency components. As a result, the number of photons required to achieve a certain signal-to-noise-ratio in the Fourier domain is reduced, thus enhancing the overall resolution in the photon-starved regime. We demonstrate our method in microscopy, achieving 5-fold improvement of Fisher information on high spatial-frequency components. Unlike active super-resolution methods, FDD is passive, making it broadly applicable in microscopy and other imaging scenarios where active illumination is impractical, including astronomy and remote sensing. Our work establishes a general strategy for designing quantum optimized superresolution imaging systems, bridging fundamental quantum limits, practical image analysis and computer vision applications.
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.
Summary form only given. To achieve super-resolution one must take into account a priori information about localization of the object. Such an a priori information exists in the case of an object of finite size. Its Fourier transform located in the focal plane of the lens is an entire analytic function, and analytic continuation of the object spectrum outside the spatial-frequency band allows for unlimited resolution. However such a super-resolution is extremely sensitive to the noise in the detected image. The ultimate limit of super-resolution is determined by the quantum fluctuations of light in the detection plane. We present the quantum theory of super-resolution for a one-dimensional coherent optical imaging scheme and discuss possibilities of improving the resolution limit by using multimode squeezed light. For quantum-mechanical description of this scheme we take into account the vacuum fluctuations of the electromagnetic field in the input plane outside the object. Interference of these vacuum fluctuations with the field amplitude of the object in the detection plane is the origin of the standard quantum limit or shot noise of photodetection in the image. To go beyond this limit we suggest to illuminate the object with multimode squeezed light having the spot size much larger than the object area. Then the vacuum fluctuations outside the object can be effectively suppressed resulting in sub-shot-noise detection of the image.
Quantum information theory has opened a new paradigm in the field of optical imaging, establishing the narrative that pre-processing the information bearing light following a quantum optimal detection strategy can achieve the fundamental performance limit. In this dissertation, we apply this narrative to study two important imaging areas : (1) passive optical superresolution imaging and (2) beam-displacement active optical sensing. Over the past decade, passive optical superresolution imaging has been extensively studied using the canonical problem of resolving two incoherent point sources. Direct detection suffers from Rayleigh’s curse when the separation goes below the Rayleigh criterion, whereas performing Spatial Mode Demultiplexing (SPADE), a quantum optimal detection strategy, gets rid of this curse, refuting Rayleigh’s minimum resolution formula. SPADE is built with multiple stratified phase masks in a multi-plane light-conversion (MPLC) setup. In the first part of this dissertation, we study how placing a single-phase mask at the pupil plane of an imaging system can affect its resolution under direct detection. We use the Classical Fisher Information (CFI) as the information metric to quantify the performance of separation estimation. Also known as PSF Engineering, we find that while this method improves the small-separation Fisher Information scaling for Gaussian PSFs (a zero-less PSF), it is not able to do the same for PSFs with zeros (Sinc PSF/hard aperture). We also study this behavior from the perspective of hypothesis testing between one versus two-point sources and derive the Bhattacharyya exponent. After this, we explore sparse aperture configurations for the hypothesis test between one versus two-point source discrimination problem. We also analyze the separation estimation problem under atmospheric turbulence and low-order wavefront correction to study the robustness of direct detection and BSPADE (Binary SPADE) performance. The atmospheric turbulence is realized using phase masks. We find that under low to moderate turbulence, BSPADE offers an advantage over direct detection measurement. We also present a Photomagnetically actuated deformable mirror (PMADM) design which can be useful for low-order wavefront correction. In the second part of the thesis, we study coherent beam displacement sensing, an active optical sensing problem. We study a free-space propagation channel with soft Gaussian apertures that supports Hermite–Gaussian (HG) modes, with the relative displacement between the apertures representing the change to be detected. Classical relative entropy (CRE) between the pre-change and post-change measurement distributions is used as the performance metric as a larger relative entropy corresponds to a shorter asymptotic change detection delay. We show that coherent probe and mode engineering strategies can increase this relative entropy and thereby reduce detection latency. In particular, we compare an optimized classical coherent probe with a spray-painted probe in which a small quantum resource (squeezing) is distributed across an optimized coherent spatial mode. We evaluate the performance using the CRE between the probability distributions of the pre-change and post-change states produced by phase matched homodyne detection. Together, these results support a unified view of pre-processing the information bearing light and using it for optical superresolution and optical sensing purposes. The dissertation explores methods such as PSF, aperture, and modal engineering, which can find applications ranging from astronomy and microscopy to optomechanical sensing.
The resolution of optical imaging devices is ultimately limited by the diffraction of light. To circumvent this limit, modern superresolution microscopy techniques employ active interaction with the object by exploiting its optical nonlinearities, nonclassical properties of the illumination beam, or near field probing. Thus, they are not applicable whenever such interaction is not possible, for example, in astronomy or noninvasive biological imaging. Far field, linear optical superresolution techniques based on passive analysis of light coming from the object would cover these gaps. In this Letter, we present the first proof-of-principle demonstration of such a technique for 2D imaging. It works by accessing information about spatial correlations of the image optical field and, hence, about the object itself via measuring projections onto Hermite-Gaussian transverse spatial modes. With a basis of 21 spatial modes in both transverse dimensions, we perform two-dimensional imaging with twofold resolution enhancement beyond the diffraction limit.
Recovering both amplitude and phase information from a system is a fundamental goal of optical imaging. At the same time, it is crucial to operate at low photon doses to avoid altering the sample, particularly in biological applications. Quantum imaging provides a powerful route to extract more information per photon than classical techniques, which are ultimately limited by shot-noise. However, the trade-off between quantum noise reduction and spatial resolution has long been regarded as a major obstacle to the application of quantum techniques to small cellular and sub-cellular structures, where they could offer the greatest benefits. Here, we overcome this limitation by demonstrating sub-shot-noise quantitative phase imaging of biological cells based on the transport-of-intensity equation, enabling high-fidelity, label-free imaging of key cellular and sub-cellular features. We achieve high-resolution phase imaging limited only by the numerical aperture, while simultaneously obtaining a resolution-independent quantum advantage. Unlike other quantum imaging approaches, our method operates in a quasi-single-shot, wide-field configuration, retrieves both phase and amplitude information, and does not rely on interferometric measurements, making it intrinsically fast and stable. These results pave the way for the immediate application of sub-shot-noise imaging in biological microscopy.
Direct imaging, which records the light intensity but discards information about the phase in the image plane, is just one among an infinite number of measurement protocols permitted by quantum mechanics. We calculate the Quantum Fisher Information (QFI) for shot-noise-limited imagery that can localize and resolve closely spaced point sources fully in all three dimensions. We also propose an experimental approach based on the use of computer generated hologram and projective measurements to realize QFI-limited variance for this problem at a qualitatively reduced photon cost. In spite of the classical character of such a measurement scheme, it achieves quantum limited performance that can be of much practical value under photon-starved operating conditions.