Abstract: 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.

Abstract: We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schrödinger model with disordered electrostatic potential, we demonstrate that the MLL, defined via a modified landscape function incorporating magnetic effects, captures key features of quantum state localization. The MLL effective potential reveals the spatial confinement regions and provides predictions of eigenstate energies, particularly in regimes where traditional semiclassical approximations break down. Numerical simulations show that below a critical energy, states localize around minima of the effective potential, while above it they cluster around maxima—with edge effects becoming significant near boundaries. Bridging the gap between semiclassical intuition and full quantum models, the MLL offers a robust framework to understand transport and localization in disordered quantum Hall systems and extends the applicability of landscape theory to magnetic systems.

Abstract: In recent years, the segmentation of short molecular trajectories with varying diffusive properties has drawn particular attention of researchers, since it allows studying the dynamics of a particle. In the past decade, machine learning methods have shown highly promising results, also in changepoint detection and segmentation tasks. Here, we introduce a novel iterative method to identify the changepoints in a molecular trajectory, i.e. frames, where the diffusive behavior of a particle changes. A trajectory in our case follows a fractional Brownian motion and we estimate the diffusive properties of the trajectories. The proposed Bottom-up iterative anomalous diffusion detector (BI-ADD) combines unsupervised and supervised learning methods to detect the changepoints. Our approach can be used for the analysis of molecular trajectories at the individual level and also be extended to multiple particle tracking, which is an important challenge in fundamental biology. We validated BI-ADD in various scenarios within the framework of the 2nd anomalous diffusion challenge 2024 dedicated to single particle tracking. Our method is implemented in Python and is publicly available for research purposes.