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Using an aluminum gallium arsenide microring resonator, we demonstrate a bright quantum optical microcomb with >300 nm (>40 THz) bandwidth and more than 20 sets of time–energy entangled modes, enabling spectral demultiplexing with simple, off-the-shelf commercial telecom components. We report high-rate continuous entanglement distribution for two sets of entangled-photon pair frequency modes exhibiting up to 20 GHz/mW²pair generation rate. As an illustrative example of entanglement distribution, we perform a continuous-wave time-bin quantum key distribution protocol with 8 kbps sifted key rates while maintaining less than 10% error rate and sufficient two-photon visibility to ensure security of the channel. When the >20 frequency modes are multiplexed, we estimate >100 kbps entanglement-based key rates or the creation of a multi-user quantum communications network. The entire system requires less than 110 µW of on-chip optical power, demonstrating an efficient source of entangled frequency modes for quantum communications. As a proof of principle, a quantum key is distributed across 12 km of deployed fiber on the University of California Santa Barbara (UCSB) campus and used to encrypt a 21 kB image with <9% error.