Spatial nonlocality imaging via metasurface

Certifying quantum nonlocality across spatially multimode fields is essential for high-dimensional quantum information, yet it remains experimentally challenging. Traditional Bell tests require repeated projective measurements for every spatial mode, leading to a quadratic increase in measurement time as resolution improves. This paper addresses the fundamental trade-off between spatial resolution and the resource cost of certifying entanglement, aiming to visualize nonlocality as a spatially distributed property rather than a global scalar.

The researchers developed a hybrid hardware-algorithmic framework to perform spatially resolved Bell tests. On the hardware side, they utilized a single-layer metasurface to perform parallel polarization projections, mapping multiple Pauli measurement outcomes onto spatially separated focal spots. This eliminates the need for sequential basis switching. On the algorithmic side, they introduced a deep-learning framework called Quantum-SFNet. This network processes sparse, photon-starved coincidence data to reconstruct the spatial distribution of the CHSH Bell parameter, enforcing physical constraints such as Hermiticity and positive semi-definiteness during the reconstruction process.

The study successfully mapped the two-dimensional spatial distribution of Bell violations across a 400-pixel biphoton field. By using the metasurface-based parallelization and the neural network, the team achieved high-resolution nonlocality imaging with an average of only 1.7 detected coincidence pairs per pixel per basis. The results demonstrate that nonlocality is highly dependent on spatial resolution; coarse-grained detection often masks genuine quantum correlations that are only revealed when the imaging resolution matches the characteristic length scale of the entangled state. The team also showed that different measurement settings produce distinct spatial nonlocality patterns, confirming the measurement-dependent nature of these correlations.