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

Abstract

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 I) 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-direct(eta) = log2(1-eta)approximate to(1/ln 2)eta bits per mode for eta << 1, beyond a certain total range L, where eta similar to 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-direct(eta), from similar to 10(11) to similar to 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.