All-photonic quantum key distribution beyond the single-repeater bound

Quantum protocols require classical signaling, and when classical signals propagate faster than quantum ones, standard rate-loss limits can be surpassed. We introduce an all-photonic measurement-device-independent quantum key distribution protocol that exceeds the single-repeater bound without error correction. When quantum signals travel at two-thirds the classical speed, the key rate scaling approaches $η^{2/5}$. We propose a single-rail, temporally multiplexed architecture that extends twin-field-type protocols to multiple nodes and surpasses their key rate without ideal quantum memories.