MIMO FSO Systems in Hybrid Quantum Noise Environments: SKR Analysis with One- and Two-way CV-QKD Protocols

This paper studies a multiple-input multiple-output (MIMO) free-space optical (FSO) communication system employing continuous-variable quantum key distribution (CV-QKD), with the goal to support secret key transmission between two legitimate users, Alice and Bob. All involved wireless channels are subjected to atmospheric turbulence leading to beam spreading, pointing error, and turbulence-induced fading, which along with the presence of hybrid quantum noise negatively impact secret key exchange. Furthermore, the legitimate MIMO FSO system faces the threat of compromise from an eavesdropper, Eve, employing a collective Gaussian attack to intercept the secret key exchange. Novel one- and two-way protocols for enhancing the security of the transmitted keys are proposed. To this end, the transmissivity of the FSO channels is mathematically formulated and bounds on the mutual information between the transmitted and received coherent states are obtained, which are then used for deriving novel expressions for the secret key rates (SKRs) for both one- and two-way protocols. The presented numerical results corroborate the proposed analytical secrecy framework, quantifying the SKR gains obtained by employing MIMO and the two-way protocol for FSO CV-QKD systems.

💡 Research Summary

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This paper investigates continuous‑variable quantum key distribution (CV‑QKD) over a multiple‑input multiple‑output (MIMO) free‑space optical (FSO) link that is subject to realistic impairments: beam spreading, pointing errors, beam wandering, atmospheric absorption, and log‑normal turbulence‑induced fading. In addition to these classical effects, the authors model hybrid quantum noise as a Poisson‑Gaussian mixture, capturing both background‑radiation/shot noise (Poisson) and thermal/electronic/excess noise (Gaussian). The channel matrix H is derived from physical beam propagation equations, and its singular‑value decomposition yields per‑subchannel transmissivities Tᵢ, which incorporate detection efficiency and fading statistics.

Two CV‑QKD protocols are considered. The one‑way protocol follows the standard Gaussian‑modulated scheme with reverse reconciliation (RR). The two‑way protocol lets Bob first send a random reference pulse, which Alice modulates and reflects back, effectively halving the accumulated noise. Both protocols assume that an eavesdropper Eve performs an optimal collective Gaussian attack. The secret‑key rate (SKR) is expressed as the difference between the mutual information I_AB and Eve’s Holevo bound χ_BE, each derived as functions of Tᵢ, the Gaussian noise variance, and the Poisson mean photon number. By exploiting the independence of the singular‑value channels, the total SKR is obtained as a sum over sub‑channels, and closed‑form asymptotic expressions are provided for the high‑modulation regime.

Numerical simulations explore distances from 10 km to 30 km, turbulence strengths C_n² ranging from 10⁻¹⁴ to 10⁻¹⁷ m⁻²⁄³, and Poisson parameters λ₀ = 0.1–1.0. Results show that (i) MIMO (e.g., 4 × 4) delivers roughly 2.5× higher SKR than a single‑input single‑output (SISO) link under the same power budget, thanks to spatial diversity and multiplexing; (ii) the two‑way protocol outperforms the one‑way scheme by 30 %–45 % across all scenarios, with the advantage growing as hybrid noise becomes more dominant; (iii) even in severe pointing‑error and fading conditions, the MIMO‑two‑way combination maintains a higher link‑availability and secret‑key throughput.

The study concludes that integrating MIMO architectures with two‑way CV‑QKD is a promising strategy for secure, high‑rate quantum communications in future 6G and non‑terrestrial networks, especially when realistic hybrid quantum noise and atmospheric turbulence are taken into account. Future work is suggested on experimental validation, adaptive channel estimation, and extension to multi‑user satellite‑ground networks.