High-Dimensional Quantum Key Distribution via full Core-mode Encoding over Deployed Multicore Fibers

Quantum key distribution (QKD) provides information-theoretic security rooted in quantum physics, while high-dimensional (HD) encoding increases both noise tolerance and secret-key yield. Multicore fibers (MCFs), a leading platform for next-generation telecom networks, are a natural substrate for HD-QKD. Field demonstrations over deployed MCFs have so far relied on a hybrid qudit encoding strategy that combines two path (core modes) with the time-bin photonic degree of freedom, rather than exploiting the full set of available core modes. Although practical, this approach incurs intrinsic efficiency penalties that grow with dimension. Here we implement a four-dimensional ($d=4$) QKD protocol that directly exploits the full set of core modes of a four-core MCF, operating over an installed MCF network across the Universidad de Concepci\'on campus under continuous environmental perturbations. We further benchmark the scheme using superconducting nanowire detectors at $10\,$dB channel loss, achieving a composable finite-key rate of $R = 6.19\times 10^{-3}\,$bits/pulse, the highest per-pulse rate reported to date for HD-QKD at comparable loss. This result establishes core-mode encoding as a viable architecture for realistic, high-rate quantum-secure communications.