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We present a resource-performance tradeoff of an all-optical quantum repeaterthat uses photon sources, linear optics, photon detectors and classicalfeedforward at each repeater node, but no quantum memories. We show that thequantum-secure key rate has the form $R(\eta) = D\eta^s$ bits per mode, where$\eta$ is the end-to-end channel's transmissivity, and the constants $D$ and$s$ are functions of various device inefficiencies and the resource constraint,such as the number of available photon sources at each repeater node. Even withlossy devices, we show that it is possible to attain $s < 1$, and in turnoutperform the maximum key rate attainable without quantum repeaters, $R_{\rmdirect}(\eta) = -\log_2(1-\eta) \approx (1/\ln 2)\eta$ bits per mode for $\eta\ll 1$, beyond a certain total range $L$, where $\eta \sim e^{-\alpha L}$ inoptical fiber. We also propose a suite of modifications to a recently-proposedall-optical repeater protocol that ours builds upon, which lower the number ofphoton sources required to create photonic clusters at the repeaters so as tooutperform $R_{\rm direct}(\eta)$, from $\sim 10^{11}$ to $\sim 10^{6}$ photonsources per repeater node. We show that the optimum separation between repeaternodes is independent of the total range $L$, and is around $1.5$ km forassumptions we make on various device losses.

Rate-distance tradeoff and resource costs for all-optical quantum repeaters