Exploiting Spatial Diversity in Earth-to-Satellite Quantum-Classical Communications

TL;DR

This work analyzes spatial diversity as a fading-mitigation strategy for Earth-to-satellite uplink CV quantum communications within a simultaneous quantum-classical signaling framework. It proposes an $M\times M$ diversity scheme with multiple ground stations and satellite apertures, and analyzes entanglement distribution and coherent-state transfer under atmospheric fading using theory and phase-screen simulations. The authors show that diversity reduces fluctuation-induced non-Gaussian noise, yielding improved Gaussian entanglement measures $E_{LN}$ and $\mathcal{R}_C$, and higher fidelities for both large-classical and small-quantum modulations, under realistic channel conditions. The results provide the first quantitative validation that spatial diversity, a classical technique, benefits uplink CV quantum communications and offer practical guidance for integrating SQCC and CV-QKD over fading channels toward a global quantum internet.

Abstract

Despite being an integral part of the vision of quantum Internet, Earth-to-satellite (uplink) quantum communications have been considered more challenging than their satellite-to-Earth (downlink) counterparts due to the severe channel-loss fluctuations (fading) induced by atmospheric turbulence. The question of how to address the negative impact of fading on Earth-to-satellite quantum communications remains largely an open issue. In this work, we explore the feasibility of exploiting spatial diversity as a means of fading mitigation in Earth-to-satellite Continuous-Variable (CV) quantum-classical optical communications. We demonstrate, via both our theoretical analyses of quantum-state evolution and our detailed numerical simulations of uplink optical channels, that the use of spatial diversity can improve the effectiveness of entanglement distribution through the use of multiple transmitting ground stations and a single satellite with multiple receiving apertures. We further show that the transfer of both large (classically-encoded) and small (quantum-modulated) coherent states can benefit from the use of diversity over fading channels. Our work represents the first quantitative investigation into the use of spatial diversity for satellite-based quantum communications in the uplink direction, showing under what circumstances this fading-mitigation paradigm, which has been widely adopted in classical communications, can be helpful within the context of Earth-to-satellite CV quantum communications.

Figures (8)

• Figure 1: System model for our calculations. We assume that only the statistics of the channel is known through some a priori channel estimation program.
• Figure 2: Scaled logarithmic negativity $E_{\text{LN}}^{(M)}$ achieved by diversity-assisted entanglement distribution under different zenith angles ${\theta_{\text{z}}=0^{\circ}}$ (solid), ${\theta_{\text{z}}=30^{\circ}}$ (dashed), and ${\theta_{\text{z}}=45^{\circ}}$ (dotted) in a real-world uplink quantum communication system. The results are plotted against the number of subchannels $M$, and different values of the quadrature variance $V_{\text{s}}$ of Alice's initial TMSV state are considered. All subchannels are modelled via our phase-screen simulations, with the excess noise referring to Alice set to ${\epsilon_j^{\mathrm{A}}=0.03\,\text{SNU}}$. The statistics of the subchannel loss in terms of $\{\text{Mean Loss},\,\text{Fading Strength}\}$ are $\{35.2\,\text{dB},\,5.8\,\text{dB}\}$ under ${\theta_{\text{z}}=0^{\circ}}$, $\{37.6\,\text{dB},\,6.2\,\text{dB}\}$ under ${\theta_{\text{z}}=30^{\circ}}$, and $\{40.4\,\text{dB},\,6.4\,\text{dB}\}$ under ${\theta_{\text{z}}=45^{\circ}}$ (the corresponding PDFs of loss are presented in Fig. \ref{['fig:PDF_Loss']}). Note that the $M=1$ data points represent the performance achieved without using diversity and are plotted as a benchmark.
• Figure 3: RCI $\mathcal{R}_{\text{C}}^{(M)}$ achieved by diversity-assisted entanglement distribution under different zenith angles ${\theta_{\text{z}}=0^{\circ}}$ (solid), ${\theta_{\text{z}}=30^{\circ}}$ (dashed), and ${\theta_{\text{z}}=45^{\circ}}$ (dotted) in a real-world uplink quantum communication system. The results are plotted against the quadrature variance of Alice's initial TMSV state $V_{\text{s}}$, and different numbers of subchannels $M$ are considered. All subchannels are modelled via our phase-screen simulations, with the excess noise referring to Alice set to ${\epsilon_j^{\mathrm{A}}=0.03\,\text{SNU}}$. The statistics of the subchannel loss in terms of $\{\text{Mean Loss},\,\text{Fading Strength}\}$ are $\{35.2\,\text{dB},\,5.8\,\text{dB}\}$ under ${\theta_{\text{z}}=0^{\circ}}$, $\{37.6\,\text{dB},\,6.2\,\text{dB}\}$ under ${\theta_{\text{z}}=30^{\circ}}$, and $\{40.4\,\text{dB},\,6.4\,\text{dB}\}$ under ${\theta_{\text{z}}=45^{\circ}}$ (the corresponding PDFs of loss are presented in Fig. \ref{['fig:PDF_Loss']}).
• Figure 4: Performance (average fidelity) of the diversity-assisted transfer of BPSK-modulated large coherent states with $\alpha$ ranging from $10$ ($100$ photons) to $50$ ($2500$ photons). All the subchannels are modelled using our log-normal model, with the excess noise referring to Alice set to $\epsilon_j^{\mathrm{A}}=0.03\,\text{SNU}$. The mean subchannel loss and the fading strength are set to $3\,\text{dB}$ and $1\,\text{dB}$, respectively. Note that the $M=1$ data points represent the performance achieved without using diversity and are plotted as a benchmark.
• Figure 5: Performance (average fidelity) of the diversity-assisted transfer of small quantum-modulated coherent states with typical values of modulation variance $V_{\text{mod}}$. All the subchannels are modelled using our log-normal model, with the excess noise referring to Alice set to $\epsilon_j^{\mathrm{A}}=0.03\,\text{SNU}$. The mean subchannel loss and the fading strength are set to $3\,\text{dB}$ and $1\,\text{dB}$, respectively. Note that the $M=1$ data points represent the performance achieved without using diversity and are plotted as a benchmark.