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.

💡 Research Summary

This paper investigates the performance of satellite‑based quantum entanglement distribution under realistic free‑space optical channels. Two network topologies are considered: (i) a triple‑satellite configuration in low‑Earth orbit (LEO) where Alice, Bob, and a relay Charlie are each on a satellite, and (ii) a ground‑satellite‑ground configuration where two terrestrial stations (Alice and Bob) communicate via a single LEO relay (Charlie). For each topology the authors compare two fundamental distribution schemes. In the “relay” scheme the entangled resource is generated at Alice (or Bob) and one half is sent to Charlie, who forwards it unchanged (or performs entanglement swapping). In the “distribution” scheme the central node Charlie creates the entangled pair and sends each half directly to the end users. Both continuous‑variable (CV) and single‑rail discrete‑variable (DV) entangled states are examined.

A central technical element is the use of probabilistic noiseless linear amplification (NLA), implemented as a first‑order quantum scissor (tele‑amplification). The NLA can boost the amplitude of a weak quantum signal without adding noise, at the cost of a non‑unit success probability. The authors quantify the entanglement generation rate as
R = p · max{I→AB, I←AB},
where p is the protocol’s heralded success probability and I→AB (I←AB) is the coherent information from Alice to Bob (or vice‑versa). This quantity provides a lower bound on the distillable entanglement per channel use.

For the symmetric triple‑satellite network the optical links are modeled as deterministic pure‑loss channels with transmissivity η. The authors find that the direct distribution scheme scales as O(η²), whereas the relay scheme with distributed NLA scales as O(η). Consequently, the NLA‑enhanced relay protocol yields a substantially higher rate for both CV and DV resources, despite the probabilistic nature of the amplification.

In the ground‑satellite‑ground scenario the uplink and downlink experience different stochastic losses due to atmospheric turbulence, beam diffraction, zenith angle, and weather. The authors generate probability density functions T_atm(η) for uplink and downlink transmissivities using realistic atmospheric parameters for a 500 km LEO satellite at zenith angles of 0°, 10°, 20°, and 30°. Because uplink loss is typically larger and more variable, the scaling advantage of the relay scheme (O(η)) can be offset by the higher average loss. Numerical simulations show that the direct distribution scheme, especially with DV entanglement, outperforms the NLA‑assisted relay configuration. DV states are more robust to turbulence and the NLA’s low success probability reduces the overall rate in this asymmetric setting.

Overall, the study concludes that: (1) for a symmetric triple‑satellite network the optimal strategy is a distributed NLA protocol, applicable to either CV or DV resources; (2) for a ground‑satellite‑ground network the optimal strategy is to generate DV entanglement centrally at the relay and distribute it without NLA. These findings provide concrete guidance for the design of future global quantum networks, indicating when to employ probabilistic amplification and which type of entangled resource (CV vs. DV) is preferable given the specific channel characteristics.