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

TL;DR

The paper tackles entanglement distribution over satellite-enabled quantum networks, comparing two core strategies—relay-based entanglement swapping and distributed entanglement via central generation—across both discrete-variable and continuous-variable resources. It develops a framework that includes unamplified and amplified (via first-order NLAs/quantum scissors) protocols, and extends the analysis to realistic free-space atmospheric channels using split-step beam propagation with HV-5/7 turbulence. Distillable-entanglement rates are bounded by coherent-information-based measures, revealing that in vacuum networks the relay with NLAs outperforms distribution, while in ground-to-satellite scenarios atmospheric fading shifts the advantage toward distributing DV entanglement via downlinks and applying local amplification. The findings offer practical guidance for designing satellite-assisted quantum networks, highlighting when downlink-focused DV distribution is preferable and detailing the impact of channel fading, amplification efficiency, and resource type on achievable rates.

Abstract

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.

Figures (5)

• Figure 1: Protocol diagrams for the triple-satellite network, where Alice, Bob and Charlie each operate a satellite in low-Earth orbit. Alice and Bob are connected via the intermediary central satellite Charlie. The optical link between both Alice and Charlie as well as Bob and Charlie is a simple diffraction-limited beam propagating through vacuum, and is assumed to be deterministic, symmetric between Alice and Bob and directionally isotropic. Each link is modelled as a pure-loss bosonic channel of transmissivity $\eta$. In the unamplified relay configuration (a.i, b.i.) Alice generates an entangled resource, one half of which is transmitted to Charlie, who forwards it to Bob unchanged. In the amplified relay configuration (a.ii, b.ii.), Alice and Bob each generate an entangled resource and send half to Charlie, who transfers Alice's entanglement to Bob via entanglement swapping. In the distribution configuration (c.), the entangled resource is generated centrally by Charlie and transmitted to Alice and Bob, who then either do nothing (d.i.) or amplify the received state (d.ii.).
• Figure 2: Protocol diagrams for the realistic case of stochastic, asymmetric atmospheric channels. The relay (a.i, ii) and distribution (b.i, ii) protocols are identical to the amplified protocols shown in Fig. \ref{['fig:protocol_diagrams_satel']}.b.ii and \ref{['fig:protocol_diagrams_satel']}.d.ii respectively, except the channels linking each station to the central satellite has been replaced with an equivalent pure-loss channel, the transmissivity of which is drawn from a distribution dependent on the atmospheric characteristics of the beam propagation path.
• Figure 3: a. The atmospheric structure constant $C_n^2$ for the Hufnagel-Valley 5/7 model as a function of altitude $h$ for zenith angle $\theta = 0$ rad. Propagation of an optical field through the atmospheric medium is emulated via discrete phase screens, which encode the turbulent characteristics of the atmospheric volume between screens. The phase screen locations (boxes) are selected according to the equal-Rytov condition \ref{['eq:equal-rytov']}. b. Optical field intensity $\abs{\Phi_\mathrm{rec}}^2$ at the receiver plane with real-space coordinates $(x_n, y_n)$ for downlink (i.) and uplink (ii.) transmission. The initial beam profile is a Gaussian beam with beam waist $\omega_0 = 0.1$ m and wavelength $\lambda = 1550$ nm. Circles denote the receiver apertures of radius $a_r = 0.4$ m (0.15 m) in the receiver plane for downlink (uplink). The transmissivity $\eta^\mathrm{down}$ ($\eta^\mathrm{up}$) is given by the ratio of received power (received intensity integrated over the aperture) to initial power. c. Distribution of $T^\mathrm{atm}(\eta)$ of the downlink and uplink atmospheric channels for zenith height $Z = 500$ km, zenith angle $\theta = 0$ rad over $N = 10 000$ simulated propagations. Inset: fitted $T^\mathrm{atm}(\eta)$ for downlink channels with zenith height $Z = 500$ km and zenith angle $\theta = 0^\circ, 10^\circ, 20^\circ$ and $30^\circ$.
• Figure 4: Unamplified (solid lines) and amplified (dashed lines) entanglement distribution protocol rates in the symmetric triple-satellite network. Rates are optimised over all free parameters. a. Distribution of discrete-variable entanglement resource $\ket{\Psi^{DV}}$. b. Distribution of continuous-variable entanglement resource $\ket{\Psi^{CV}}$.
• Figure 5: Amplified entanglement distribution protocol rates for the relay and distribution configurations across a ground-satellite-ground network. Optimised rates are characterised over a trial of 250 random simulations of each protocol over the stochastic atmospheric channels $\mathcal{E}_A(\eta_A)$, $\mathcal{E}_B(\eta_B)$, where $\eta_A,\eta_B$ are drawn randomly from the uplink or downlink channel probability density functions in Figure \ref{['fig:pubfig_atmos_multiplot']}.c. a. Distribution of discrete-variable entanglement resource $\ket{\Psi^{DV}}$. b. Distribution of continuous-variable entanglement resource $\ket{\Psi^{CV}}$.