Emulation of satellite up-link quantum communication with entangled photons

TL;DR

The paper tackles the challenge of enabling long-distance quantum communication via up-link satellite configurations using entangled photons, avoiding trusted ground stations. It presents an ultra-bright, far non-degenerate entangled-photon source that operates at $785$ nm and $1572$ nm and emulates high-loss LEO up-links by combining atmospheric and terrestrial channels, demonstrating secure key generation under realistic loss budgets. Key results include SKR up to $113$ bps without terrestrial fibre and $33.9$ bps with 10 km fibre, yielding overpass keys of $18{,}146$ and $5{,}223$ bits, respectively, and a notable gain from real-time optimization to $61.5$ bps and $9{,}768$ bits per overpass. The study also analyzes how state fidelity and heralding efficiency constrain the loss budget, suggesting practical improvements (e.g., higher heralding efficiency, adaptive optics) that can further elevate SKR, thereby informing the design of upcoming low-Earth orbit receiver missions and satellite quantum networks: $\mathrm{SKR} = \frac{CC}{2} \left(1 - h(QBER) - h(Q_x)\right)$.

Abstract

Quantum communication rates in terrestrial quantum networks are fundamentally limited by fibre loss, even in the presence of quantum repeaters. Satellites offer a solution for long-distance communication, with the most commonly explored scenario involving prepare-and-measure protocols connecting from orbit to a trusted-node ground station via free-space down-links. In contrast, up-link scenarios allow for entanglement to be distributed between a satellite and remote end users in terrestrial networks, eliminating any trust requirement on the ground station. Here we demonstrate an ultra-bright source of far-non-degenerate entangled photons and perform quantum key distribution in emulated high-loss satellite scenarios. With a loss profile corresponding to that of one of the pioneering Micius up-link experiments, and a terrestrial end user separated by 10~km of telecom fibre we achieve secure key bit accumulation of 5.2~kbit in a single emulated overpass in the asymptotic limit. Our results confirm the viability of upcoming low-Earth orbit receiver satellite missions.

Figures (9)

• Figure 1: Schematic for conducting up-link QKD with an overpassing satellite. The EPS located at the OGS distributes entangled photons between an overpassing satellite and an end-user located in a network, Alice, allowing them to generate a secret key $k_{\text{A}}$. The satellite, a trusted node, then travels to another end-user, Bob, and they similarly generate $k_{\text{B}}$. The satellite now uses $k_{\text{B}}$ as a one-time-pad to encode $k_{\text{A}}$ and securely share it with Bob.
• Figure 2: Experimental schematic. (a) Entangled photon source (description in main text). (b) The telecom photon is transmitted through 10 km of fibre whilst the 785 nm photon is transmitted through a free-space channel. The free-space channel contains a variable loss wheel, which is mounted to a motorised controller to emulate the loss profile of an overpassing satellite. (c) After the fibre and free-space channel transmission respectively, the entangled photons are measured in either the Pauli-$Z$ or Pauli-$X$ bases to perform the BBM92 quantum communication protocol. A random basis choice is made by a balanced beam-splitter (BS) and photons are projected into the Pauli-$Z$ basis using a polarising beam-splitter (PBS) or projected into the Pauli-$X$ basis using a half-wave-plate (HWP) and a PBS. After projection, the photons are again coupled into single-mode fibres, the telecom photons are detected by superconducting nanowire single-photon detectors (SNPDs) and the $785$ nm photons are detected using Silicon single photon avalanche detectors (Si-APDs). Detection events are tagged with a time stamp by a time-tagging unit, and the tags are subsequently processed to identify detection events that correspond to coincidence events.
• Figure 3: Secure key rate estimates with 10 km fibre. Top: SKR in the asymptotic limit as a function of satellite up-link loss, with a fixed coincidence window for different pump powers. Bottom: SKR in the asymptotic limit versus link loss for two different Si-APD dark count rates. The SKR is non-zero up to $\sim$ 35 dB with a dark count rate of 250 cps, and up to $\sim$ 45 dB with a dark count rate of 1400 cps. The solid and dashed lines are the simulated results using the model contained in Ref. neumann for our experimental parameters. Data points are evaluated via Eq. (\ref{['eq:SKR']}).
• Figure 4: Experimental up-link emulation. To determine the anticipated key length from an overpass via an up-link channel we extract the empirical channel loss data from Ref. ren_ground--satellite_2017, plotted as the black line. Combining our results, the modelling work in Ref. neumann and the extracted channel loss, the purple and dark blue lines show how the SKR varies as a function of time for the scenarios with 0 km and 10 km of telecom fibre spool attached, at a fixed pump power of 5 mW. Without terrestrial fibre, the asymptotic key rate peaks at 113 bps creating an integrated key of 18146 bits in one overpass. When the terrestrial photons travel through 10 km of fibre, the SKR peaks at 33.9 bps and integrates to a key of 5223 bits in one overpass.
• Figure S1: (a) Contour plot of the theoretical SKR given our system parameters assuming no dispersion. (b) Contour plot of the theoretical SKR given our system parameters assuming a dispersion of 18 ps/km.