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Performance Analysis of Satellite-Based QKD Protocols Using the Circular Beam Model

Muskan, Ramniwas Meena, Subhashish Banerjee

TL;DR

This work assesses the performance of four QKD protocols—BB84, B92, BBM92, and E91—over low-Earth-orbit satellite links using a circular beam transmittance model that captures diffraction, pointing errors, atmospheric turbulence, and background photons. By combining this channel model with MODTRAN6 transmittance data and realistic stray-light assumptions, the authors derive protocol-specific QBER and asymptotic key-rate formulas (e.g., $R_{BB84}$, $R_{B92}$, $R_{BBM92}$, $R_{E91}$) and analyze uplink versus downlink behavior under day and night conditions. The results show that downlink channels consistently offer lower QBER and higher key rates than uplink, with BB84 outperforming B92 and BBM92 outperforming E91, while key rates generally decay with increasing zenith angle. These findings provide practical guidance for selecting QKD protocols and link configurations in future space-based quantum networks, highlighting BB84 and BBM92 as robust choices for high-rate global quantum communication. $\,$

Abstract

Satellite-based free-space quantum key distribution (QKD) provides a practical framework for achieving secure global communication beyond the limitations of optical fibers. In this work, the quantum bit error rate (QBER) and secure key rate of four representative protocols-BB84, B92, BBM92, and E91 are investigated over low earth orbit (LEO) links in both uplink and downlink configurations. A circular beam transmittance model is employed, incorporating the effects of diffraction, pointing errors, atmospheric turbulence, and background photons. The protocols are examined under day and night-time operating conditions, and their dependence on the zenith angle is analyzed. The findings show that downlink links generally exhibit lower QBER and higher secure key rates than uplinks, and among prepare-and-measure schemes, BB84 consistently outperforms B92, while in entanglement-based approaches, BBM92 achieves higher key rates than E91.

Performance Analysis of Satellite-Based QKD Protocols Using the Circular Beam Model

TL;DR

This work assesses the performance of four QKD protocols—BB84, B92, BBM92, and E91—over low-Earth-orbit satellite links using a circular beam transmittance model that captures diffraction, pointing errors, atmospheric turbulence, and background photons. By combining this channel model with MODTRAN6 transmittance data and realistic stray-light assumptions, the authors derive protocol-specific QBER and asymptotic key-rate formulas (e.g., , , , ) and analyze uplink versus downlink behavior under day and night conditions. The results show that downlink channels consistently offer lower QBER and higher key rates than uplink, with BB84 outperforming B92 and BBM92 outperforming E91, while key rates generally decay with increasing zenith angle. These findings provide practical guidance for selecting QKD protocols and link configurations in future space-based quantum networks, highlighting BB84 and BBM92 as robust choices for high-rate global quantum communication.

Abstract

Satellite-based free-space quantum key distribution (QKD) provides a practical framework for achieving secure global communication beyond the limitations of optical fibers. In this work, the quantum bit error rate (QBER) and secure key rate of four representative protocols-BB84, B92, BBM92, and E91 are investigated over low earth orbit (LEO) links in both uplink and downlink configurations. A circular beam transmittance model is employed, incorporating the effects of diffraction, pointing errors, atmospheric turbulence, and background photons. The protocols are examined under day and night-time operating conditions, and their dependence on the zenith angle is analyzed. The findings show that downlink links generally exhibit lower QBER and higher secure key rates than uplinks, and among prepare-and-measure schemes, BB84 consistently outperforms B92, while in entanglement-based approaches, BBM92 achieves higher key rates than E91.
Paper Structure (20 sections, 29 equations, 4 figures, 1 table)

This paper contains 20 sections, 29 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. QKD Protocols
  3. BB84
  4. B92
  5. E91
  6. BBM92
  7. Channel Modeling
  8. Environmental Photons (stray-photons)
  9. QBER
  10. QBER for BB84
  11. QBER for B92
  12. QBER for BBM92
  13. QBER for E91
  14. Keyrate
  15. Keyrate for BB84
  16. ...and 5 more sections

Figures (4)

  • Figure 1: (a) QBER and key rate versus zenith angle for the BB84 protocol in the uplink (night-time). (b) and (c) QBER and key rate versus zenith angle for the BB84 protocol in the downlink (day-time) and downlink (night-time), respectively.
  • Figure 2: (a) QBER and key rate versus zenith angle for the B92 protocol in the uplink (night-time). (b) and (c) QBER and key rate versus zenith angle for the B92 protocol in the downlink (day-time) and downlink (night-time), respectively.
  • Figure 3: (a) QBER and key rate versus zenith angle for the BBM92 protocol in the uplink (night-time). (b) and (c) QBER and key rate versus zenith angle for the BBM92 protocol in the downlink (day-time) and downlink (night-time), respectively.
  • Figure 4: (a) QBER and key rate versus zenith angle for the E91 protocol in the uplink (night-time). (b) and (c) QBER and key rate versus zenith angle for the E91 protocol in the downlink (day-time) and downlink (night-time), respectively.