Entanglement distribution via satellite: an evaluation of competing protocols assuming realistic free-space optical channels

A key technical requirement of any future quantum network is the ability to distribute quantum-entangled resources between two spatially separated points at a high rate and high fidelity. Entanglement distribution protocols based on satellite platforms, which transmit and receive quantum resources directly via free-space optical propagation, are therefore excellent candidates for quantum networking, since the geometry and loss characteristics of satellite networks feasibly allow for up to continental-scale ($\sim10^3$ km) over-the-horizon communication without the infrastructure, cost, or losses associated with equivalent fibre-optic networks. In this work, we explore two network topologies commonly associated with quantum networks - entanglement distribution between two satellites in low-Earth orbit mediated by a third satellite and entanglement distribution between two ground stations mediated by a satellite in low-Earth orbit, and two entanglement distribution schemes - one where the central satellite is used as a relay, and the other where the central satellite is used to generate and distribute the entangled resource directly. We compute a bound on the rate of distribution of distillable entanglement achieved by each protocol in each network topology as a function of the network channels for both single-rail discrete- (DV) and continuous-variable (CV) resources and use or non-use of probabilistic noiseless linear quantum amplification (NLA). In the case of atmospheric channels we take into account the turbulent and optical properties of the free-space propagation. We determine that for the triple-satellite network configuration, the optimal strategy is to perform a distributed NLA scheme in either CV or DV, and for the ground-satellite-ground network the optimal strategy is to distribute a DV resource via the central satellite.