Programmable high-dimensional state synthesis through a 20-m multimode fiber via long-coherence atomic photons

High-dimensional photonic operations are an important resource for quantum information processing, yet achieving scalability and long-distance operation remains a formidable challenge. Here, we demonstrate reconfigurable high-dimensional spatial-mode state synthesis using spatial-mode-encoded qu d its in a 20-m-long multimode fiber. By exploiting the ultra-long coherence of heralded single photons from a warm 87 Rb atomic ensemble, we overcome the modal dispersion limits that restricted previous short-distance demonstrations. Using digital optical phase conjugation, we deterministically synthesize spatial-mode states structured by target unitary operations, including generalized Pauli operators and quantum Fourier transforms, through the complex fiber medium. We achieve process fidelities exceeding 92.5(4)% for dimensions up to d = 7. These results establish long multimode fibers as a reconfigurable platform for high-dimensional quantum state synthesis and transport in fiber-based quantum information processing.