Continuous-variable Measurement Device Independent MIMO Quantum Key Distribution for THz Communications

TL;DR

This work tackles detector-side vulnerabilities in THz CVQKD by proposing a measurement-device-independent (MDI) MIMO QKD protocol that uses transmit-receive beamforming to convert a MIMO THz link into multiple parallel SISO channels. It develops both prepare-and-measure and entanglement-based models, analyzes Gaussian collective attacks, and derives asymptotic and finite-size key rates under reverse reconciliation, with key rates characterized by $K_{ ext{MIMO}}^{Ar} = \sum_{i=1}^r K_i^A$ and, in the finite-size case, $K_{ ext{MIMO}}^{Fr} = \sum_{i=1}^r \frac{N}{M}[\beta K_i^F(\cdots) - \Delta(N)]$. Simulations show that multi-antenna configurations substantially enhance rate and distance, with optimal long-range operation at lower THz frequencies (around $0.1$ THz) and high detector efficiency; a large $1024\times1024$ MIMO at $0.1$ THz can reach about $2374$ m at room temperature. The framework provides a scalable, secure approach for next-generation wireless networks, balancing practical finite-size effects and detector imperfections for indoor and outdoor deployments.

Abstract

Although multiple-input multiple-output (MIMO) terahertz (THz) continuous-variable quantum key distribution (CVQKD) is theoretically secure, practical vulnerabilities may arise due to detector imperfections. This paper explores a CV measurement-device-independent (MDI) QKD system operating at THz frequencies within a MIMO framework. In this system, measurement is delegated to an untrusted third party, Charlie, rather than the receiver, eliminating all detector attacks and significantly enhancing the system's practical security. Using transmit-receive beamforming techniques, the system transforms MIMO channels into multiple parallel lossy quantum channels, enabling robust key distribution between Alice and Bob. This study examines entanglement-based and prepare-and-measure protocols, deriving secret key rates for both asymptotic and finite code scenarios. Simulations reveal the critical role of multiple antenna configurations and efficient homodyne detection in mitigating free-space path loss and maximizing key rates. Results indicate that system performance is optimized at lower THz frequencies for long-range transmissions and higher frequencies for short-range applications. The proposed protocol offers a scalable solution for secure quantum communications in next-generation wireless networks, demonstrating potential for deployment in both indoor and outdoor environments.

Figures (8)

• Figure 1: Schematic diagram of CVMDI protocol of the $3 \times 3$ MIMO configuration with the PM scheme where Alice and Bob's transmitter antenna nodes are connected to Charlie's receiver antenna nodes via the free space channel with the transmission of the THz wireless channel ${T_{A_i}}$,${T_{B_i}}$ and the noise variance $W_{A_i}$,$W_{B_i}$. Alice (Bob) and Charlie employ transmit-receive beamforming techniques to decompose the original MIMO channel into multiple parallel SISO channels. The TBF and RBF are transimit and receive beamforming, respectively.
• Figure 2: Key rate as a function of operating frequency for multiple MIMO configurations at room temperature when transmission distance approaches zero.
• Figure 3: Asymptotic key rate as a function of the transmission distance for the various MIMO configurations with different frequencies. As the frequency decreases from 1THz to 0.1THz, the maximum transmission distance in $1024\times 1024$ MIMO configuration gradually increases from 125m to 2374m. This trend also applies to other MIMO configurations. $\eta_{D_{A(B)_{i}}}=1$, atmospheric loss $\delta_{1,2}$: 0.6 dB/km for 0.1THz, 5 dB/km for 0.25THz, 50 dB/km for 0.5THz and 100 dB/km for 1THz.
• Figure 4: A three-dimensional surface plot showing the relationship between the $K_{\mathrm{MIMO}}^{Ar}$, homodyne detector efficiency and the transmission distance with different frequencies. All subplots, arranged from top to bottom, represent the $16\times16$, $8\times8$ and $4\times4$ MIMO configurations, respectively. atmospheric loss $\delta_{1,2}$: 0.6 dB/km for 0.1THz, 5 dB/km for 0.25THz and 50 dB/km for 0.5THz
• Figure 5: Secret key rate as a function of transmission distance for different frequencies in SISO protocol. It can be observed that, at shorter distances, higher frequency THz waves yield higher key rates. $\eta_{D_{A(B)_{i}}}=1$, atmospheric loss $\delta_{1,2}$: 0.6 dB/km for 0.1THz, 5 dB/km for 0.25THz, 50 dB/km for 0.5THz and 100 dB/km for 1THz.