Empowering Spatial‐Mode‐Encoded High‐Dimensional State Reconstruction With Parallel Full Bloch Vector Mapping

ABSTRACT Quantum state tomography plays a fundamental role in quantum information science. Spatial modes of photons offer a promising encoding platform for high‐dimensional quantum states, yet efficient reconstruction of such states remains challenging. Recent advances in diffractive neural networks (DNNs) have introduced powerful capabilities for spatial mode manipulation, offering new opportunities for realizing efficient projective measurements. Here, we propose and experimentally demonstrate an efficient high‐dimensional state reconstruction method, enabled by parallel measurement of the full Bloch vectors for high‐dimensional states encoded in spatial modes of photons. By employing a DNN, our method maps mutually unbiased basis states to spatially separated Gaussian spots, thereby performing parallel projective measurements with a single measurement setting. We successfully reconstruct spatial‐mode‐encoded states in dimensions two through four, achieving state fidelities up to 99% and measurement process fidelities up to 97%. The method is further extended to spin‐orbit non‐separable states and mixed states, demonstrating its capability for reconstructing different classes of states within the selected spatial‐mode encoding space. Our method significantly improves the efficiency of tomography for spatial‐mode‐encoded high‐dimensional states and provides a versatile tool for the rapid characterization of high‐dimensional quantum systems.