  We present a resource-performance tradeoff of an all-optical quantum repeater
that uses photon sources, linear optics, photon detectors and classical
feedforward at each repeater node, but no quantum memories. We show that the
quantum-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 with
lossy devices, we show that it is possible to attain $s < 1$, and in turn
outperform the maximum key rate attainable without quantum repeaters, $R_{\rm
direct}(\eta) = -\log_2(1-\eta) \approx (1/\ln 2)\eta$ bits per mode for $\eta
\ll 1$, beyond a certain total range $L$, where $\eta \sim e^{-\alpha L}$ in
optical fiber. We also propose a suite of modifications to a recently-proposed
all-optical repeater protocol that ours builds upon, which lower the number of
photon sources required to create photonic clusters at the repeaters so as to
outperform $R_{\rm direct}(\eta)$, from $\sim 10^{11}$ to $\sim 10^{6}$ photon
sources per repeater node. We show that the optimum separation between repeater
nodes is independent of the total range $L$, and is around $1.5$ km for
assumptions we make on various device losses.
