Quantum key distribution (QKD) can provide unconditional security to next generation communication networks guaranteed by the laws of quantum physics. This paper studies the secret key rate (SKR) of a continuous variable quantum key distribution (CV-QKD) system using multiple-input multipleoutput (MIMO) transmission and operating at Terahertz (THz) frequencies. Distinct from previous works, we consider a practical “restricted" eavesdropping scenario in which Eve can collect only a fraction of photons lost in the environment. We propose a system model for the MIMO THz CV-QKD system that accounts for restricted eavesdropping via a lossy wireless channel between Alice and Eve. We derive for this system new SKR expressions for both coherent-state-based and squeezed-state-based CV-QKD protocols. Our results show that previous analysis assuming unrestricted eavesdropping leads to overly pessimistic SKRs, and that in practice, the achievable SKR can be significantly increased under restricted eavesdropping. The increase in the SKR is quantified by the simplified SKR expansions derived in this paper. Our results also reveal that squeezing is beneficial for improving the SKR only for unrestricted eavesdropping. However, in a practical setting with restricted eavesdropping, increased squeezing leads to a reduction in the SKR.
Quantum key distribution (QKD) can provide unconditional security to next generation communication networks guaranteed by the laws of quantum physics. This paper studies the secret key rate (SKR) of a continuous variable quantum key distribution (CV-QKD) system using multiple-input multipleoutput (MIMO) transmission and operating at Terahertz (THz) frequencies. Distinct from previous works, we consider a practical “restricted" eavesdropping scenario in which Eve can collect only a fraction of photons lost in the environment. We propose a system model for the MIMO THz CV-QKD system that accounts for restricted eavesdropping via a lossy wireless channel between Alice and Eve. We derive for this system new SKR expressions for both coherent-state-based and squeezed-state-based CV-QKD protocols. Our results show that previous analysis assuming unrestricted eavesdropping leads to overly pessimistic SKRs, and that in practice, the achievable SKR can be significantly increased under restricted eavesdropping. The increase in the SKR is quantified by the simplified SKR expansions derived in this paper. Our results also reveal that squeezing is beneficial for improving the SKR only for unrestricted eavesdropping. However, in a practical setting with restricted eavesdropping, increased squeezing leads to a reduction in the SKR.
A reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) continuous-variable quantum key distribution (CV-QKD) system operating at terahertz (THz) frequencies, in which a transmitter, Alice, encodes secret keys using Gaussian-modulated coherent states and communicates them to a legitimate receiver, Bob, is considered in this paper. The composite wireless channel, comprising the direct Alice-Bob link and the RIS-assisted reflected link, is modeled as a passive linear Gaussian quantum channel, enabling a unitary dilation that preserves the canonical commutation relations. The security of the considered system is investigated under collective Gaussian entangling attacks by introducing a practical access-constrained eavesdropping model, in which an eavesdropper, Eve, is assumed to access only the environmental modes associated with physically accessible propagation segments. A unified analytical framework is developed to derive the achievable secret key rate (SKR) across all single-segment, pairwise-segment, and full-segment access scenarios, assuming homodyne detection and reverse reconciliation at Bob. Furthermore, an optimization framework is developed to determine the optimal RIS phase configuration matrix and transmitter/receiver beam-splitter parameters that maximize the SKR performance. The resulting optimization problem is efficiently solved using particle swarm optimization. Numerical results are presented to demonstrate the system's performance with respect to various free parameters. It is showcased that the secrecy performance strongly depends on Eve's accessible propagation segments, with the Alice-RIS channel constituting the most security-critical segment.
We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.
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.
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.
In this paper, a multiple-input multiple-output (MIMO) wireless system incorporating a reconfigurable intelligent surface (RIS) to efficiently operate at terahertz (THz) frequencies is considered. The transmitter, Alice, employs continuous-variable quantum key distribution (CV-QKD) to communicate secret keys to the receiver, Bob, who utilizes either homodyne or heterodyne detection. The latter node applies the least-squares approach to estimate the effective MIMO channel gain matrix prior to receiving the secret key, and this estimation is made available to Alice via an error-free feedback channel. An eavesdropper, Eve, is assumed to employ either a collective Gaussian entanglement attack or an individual attack on the feedback channel to obtain the estimated channel state information. We present novel closed-form expressions for the secret key rate (SKR) performance of the proposed RIS-assisted THz CV-QKD system. An optimization framework to obtain the optimal phase shifts of the RIS to maximize the SKR is proposed, and a particle-swarm optimization (PSO)-based algorithm is deployed to solve the optimization problem. The effect of various system parameters, such as the number of RIS elements and their phase configurations, the channel estimation error, and the detector noise, on the SKR performance is studied via numerical evaluation of the derived formula. It is demonstrated that the RIS contributes to larger SKR for larger link distances, and that heterodyne detection is preferable over homodyne at lower pilot symbol powers.
We propose a multiple-input multiple-output (MIMO) quantum key distribution (QKD) scheme for terahertz (THz) frequency applications operating at room temperature. Motivated by classical MIMO communications, a transmit-receive beamforming scheme is proposed that converts the rank-r MIMO channel between Alice and Bob into r parallel lossy quantum channels. Compared with existing single-antenna QKD schemes, we demonstrate that the MIMO QKD scheme leads to performance improvements by increasing the secret key rate and extending the transmission distance. Our simulation results show that multiple antennas are necessary to overcome the high free-space path loss at THz frequencies. We demonstrate a non-monotonic relation between performance and frequency, and reveal that positive key rates are achievable in the 10–30 THz frequency range. The proposed scheme can be used for both indoor and outdoor QKD applications for beyond fifth generation ultra-secure wireless communications systems.