High-Probability Heralded Entanglement via Repeated Spin-Photon Phase Encoding with Moderate Cooperativity

Abstract

We propose a heralded high-probability scheme to generate remote entanglement between moderate-cooperativity spin-cavity registers with high fidelity. In conventional single-shot interfaces, limited cooperativity restricts the spin-conditional optical response and thus strongly suppresses the success probability. Our proposal instead recycles a single incident photon for repeated interactions with the spin-cavity register, such that a small spin-conditional phase shift acquired on each round trip accumulates coherently to enable remote entanglement. Moreover, the repeated scheme enables higher spin-photon encoding efficiency by using a spectral-width-scaling photon pulse with a shorter duration. We show that, for realistic imperfections and losses, this repeated phase-encoding approach produces high-fidelity entangled states with an appreciable success probability even at cooperativity $C\sim1$. Our protocol is particularly well suited to weakly coupled, cavity-based solid-state spin platforms and provides a route toward hybrid, photon-loss-tolerant distributed quantum computing.