Optimization approaches are ubiquitous in physics. In optics, they are key to manipulating light through complex media, enabling applications ranging from imaging to photonic simulators. In most demonstrations, however, the optimization process is implemented using classical coherent light, leading to a purely classical solution. Here we introduce the concept of optical non-classical optimization in complex media. We experimentally demonstrate the control and refocusing of non-classical light -- namely, entangled photon pairs -- through a scattering medium by directly optimizing the output coincidence rate. The optimal solutions found with this approach differ from those obtained using classical optimization, a result of entanglement in the input state. Beyond imaging, this genuinely non-classical optimization method has potential to tackle complex problems, as we show by simulating a spin-glass model with multi-spin interactions.
Optimization approaches are ubiquitous in physics. In optics, they are key to manipulating light through complex media, enabling applications ranging from imaging to photonic simulators. In most demonstrations, however, the optimization process is implemented using classical coherent light, leading to a purely classical solution. Here we introduce the concept of optical non-classical optimization in complex media. We experimentally demonstrate the control and refocusing of non-classical light -- namely, entangled photon pairs -- through a scattering medium by directly optimizing the output coincidence rate. The optimal solutions found with this approach differ from those obtained using classical optimization, a result of entanglement in the input state. Beyond imaging, this genuinely non-classical optimization method has potential to tackle complex problems, as we show by simulating a spin-glass model with multi-spin interactions.
Optimization approaches are ubiquitous in physics. In optics, they are key to manipulating light through complex media, enabling applications ranging from imaging to photonic simulators. In most demonstrations, however, the optimization process is implemented using classical coherent light, leading to a purely classical solution. Here, we introduce the concept of optical non-classical optimization in complex media. We experimentally demonstrate the control and refocusing of non-classical light—namely, entangled photon pairs—through a scattering medium by directly optimizing the output coincidence rate. Importantly, these optimal solutions cannot be obtained with classical light and do not result in a focus for classical light; this is a result of entanglement in the input state. This genuinely non-classical optimization method promises advances in quantum imaging, communication, and optical simulations with non-classical light.
Wavefront shaping is a key technique for mitigating scattering in complex media, enabling advanced imaging and optical communication. Yet existing approaches are inherently local, requiring active correction elements - such as spatial light modulators or deformable mirrors - to lie directly in the optical path of the scattered light, which limits their integration into compact imaging systems. Here, we experimentally demonstrate nonlocal wavefront shaping using spatially entangled photon pairs. By applying a phase correction to a photon that never interacts with the scattering medium, we compensate for the distortions experienced by its entangled partner and restore their initial spatial correlations. Our approach physically decouples the wavefront correction from the scattering medium, paving the way for imaging through complex media in compact and otherwise inaccessible systems.
Wavefront shaping enables control of classical light through scattering media. Extending these techniques to spatially entangled photons promises new quantum applications, but their fundamental limits, especially when both photons scatter, remain unclear. Here, we theoretically and numerically investigate the enhancement of two-photon correlations through thick scattering media. We analyze configurations where a spatial light modulator shapes one or both photons, either before or after the medium, and show that the optimal enhancement differs fundamentally from classical expectations. For a system with N modes, we show that shaping one photon yields the classical enhancement η≈(π/4)N, while shaping both photons before the medium reduces it to η≈(π/4)2N. However, in some symmetric detection schemes, when both photons are measured at the same mode, perfect correlations are restored with η≈N, resembling digital optical phase conjugation. Conversely, shaping both photons after the medium leads to a complex, NP-hard-like optimization problem, yet achieves superior enhancements, up to η≈4.6N. These results reveal unique quantum effects in complex media and identify strategies for quantum imaging and communication through scattering environments.
Wavefront shaping enables control of classical light through scattering media. Extending these techniques to spatially entangled photons promises new quantum applications, but their fundamental limits, especially when both photons scatter, remain unclear. Here, we theoretically and numerically investigate the enhancement of two-photon correlations in two specific output modes through thick scattering media. We analyze three configurations: shaping one photon after the medium, shaping both photons before the medium, and shaping both photons after the medium. We show that each configuration yields fundamentally different enhancements compared to classical expectations. For a system with N modes, we show that shaping one photon yields the classical enhancement η ≈ (π/4)N, while shaping both photons before the medium reduces it to η ≈ (π/4)2N. However, in some symmetric detection schemes, when both photons are measured at the same mode, perfect correlations are restored with η ≈ N, resembling digital optical phase conjugation. Conversely, shaping both photons after the medium leads to a complex, NP-hard-like optimization problem, yet achieves superior enhancements, up to η ≈ 4.6N. These results reveal unique quantum effects in complex media and identify strategies for quantum imaging and communication through scattering environments.
Quantum imaging enhances imaging systems performance, potentially surpassing fundamental limits such as noise and resolution. However, these schemes have limitations and are still a long way from replacing classical techniques. Therefore, there is a strong focus on improving the practicality of quantum imaging methods, with the goal of finding real-world applications. With this in mind, in this tutorial we describe how the concepts of classical light shaping can be applied to imaging schemes based on entangled photon pairs. We detail two basic experimental configurations in which a spatial light modulator is used to shape the spatial correlations of a photon pair state and highlight the key differences between this and classical shaping. We then showcase two recent examples that expand on these concepts to perform aberration and scattering correction with photon pairs. We include specific details on the key steps of these experiments, with the goal that this can be used as a guide for building photon-pair-based imaging and shaping experiments.
Abstract Quantum imaging enhances imaging systems performance, potentially surpassing fundamental limits such as noise and resolution. However, these schemes have limitations and are still a long way from replacing classical techniques. Therefore, there is a strong focus on improving the practicality of quantum imaging methods, with the goal of finding real-world applications. With this in mind, in this tutorial we describe how the concepts of classical light shaping can be applied to imaging schemes based on entangled photon pairs. We detail two basic experimental configurations in which a spatial light modulator is used to shape the spatial correlations of a photon pair state and highlight the key differences between this and classical shaping. We then showcase two recent examples that expand on these concepts to perform aberration and scattering correction with photon pairs. We include specific details on the key steps of these experiments, with the goal that this can be used as a guide for building photon-pair-based imaging and shaping experiments.