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.
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.
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.
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, which utilizes either homodyne or heterodyne detection. The latter node applies the least-squared 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 a collective Gaussian entanglement attack on the feedback channel to avail the estimated channel state information. We present a novel closed-form expression for the secret key rate (SKR) performance of the proposed RIS-assisted THz CV-QKD system. 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 are 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.
A reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) wireless communication system is considered in this paper wherein the transmitter, Alice modulates secret keys, by using a continuous variable quantum key distribution technique to be transmitted to the receiver, Bob, which employs homodyne detection for data decoding. The data is transmitted over two paths, namely a direct path between Alice and Bob and the wireless path between them via the RIS. Transmit and receive beamsplitters are employed in the system to transform the MIMO terahertz channels into parallel single-input single-output channels. Considering an eavesdropper, Eve, to attack all the three wireless channels in the system (i.e., the direct channel, the channel between Alice and RIS, and between the RIS and Bob) but having restricted quantum memory limiting it to store the ancilla modes from either of these three wireless channels, novel expressions for the secret key rate (SKR) of the system are derived. Numerical results are presented to demonstrate the dependency of the system's performance on various system parameters. It is observed that the RIS plays a key role in increasing the SKR of the system and the transmission distance, ensuring secure communications between Alice and Bob. The significance of employing RIS is observed specifically for the case when Eve measures the ancilla modes of the channel between the RIS and Bob. Furthermore, for all such measurement scenarios, optimal angles are obtained for the phase shifts of the RIS elements to maximize the SKR for various MIMO configurations and transmission distance between Alice and Bob.
Although quantum key distribution (QKD) enables information-theoretically secure key distribution, it is mainly designed for point-to-point communication and cannot directly support multi-user collaborative scenarios. To address this limitation, quantum secret sharing (QSS) has been proposed to enable secure multiparty key sharing. However, most existing QSS protocols rely on a single-input single-output (SISO) channel, which limits the achievable secret key rate (SKR) and transmission distance. This paper proposes a continuous-variable (CV) QSS protocol based on a multiple-input multiple-output (MIMO) architecture operating in the terahertz (THz) band. In the proposed scheme, transmit-receive beamforming decomposes the MIMO channel into multiple parallel SISO subchannels, thereby improving both the SKR and transmission distance. We describe the QSS transmission procedure and derive the SKR expressions for eight protocol variants under Gaussian collective attacks. Specifically, Gaussian modulation and passive modulation are considered at the transmitter, while homodyne and heterodyne detection are considered at the receiver. Both asymptotic and composable finite-size SKR formulas are derived to characterize the ideal upper-bound performance and the achievable performance under finite resources, respectively. Simulation results show that, under ideal assumptions including perfect channel state information, perfect phase synchronization, and ideal beamforming, the Gaussian-modulation protocol with a 32 x 32 antenna configuration and the passive-modulation protocol with a 1024 x 1024 antenna configuration achieve transmission distances of 14.99 m and 160 m in the atmospheric channel, respectively. These results provide an idealized theoretical benchmark for evaluating the potential performance gains of MIMO-assisted THz CV-QSS in indoor and short-range outdoor wireless networks.
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.
In this article, the physical layer security (PLS) is investigated for reconfigurable intelligent surface (RIS)-aided wireless communication systems, where one RIS is deployed to assist the communications between a pair of transmitter (Alice) and receiver (Bob), under a passive eavesdropper (Eve) attack. For the Eve, different from the bounded channel state information uncertainty model, the distribution of the Eve’s location is introduced into the wiretap link. In the proposed system, considering that the Eve can overhear signals transmitted from Alice or reflected by the RIS, two scenarios are studied for RIS-aided secure communication systems: one is that the Eve distributes close to Alice without the RIS orientation, and the other is that the Eve locates close to Bob and in the presence of the RIS. After investigating the probability distribution functions of the Eve’s location and the wiretap link, the novel cumulative density functions (CDFs) of the received signal-to-noise ratios (SNRs) at the Eves are, respectively, derived for the two considered scenarios, taking into account the effects of RIS reflection coefficients, pathloss, and Eve’s location distribution. The closed-form expressions for the probability of the nonzero secrecy capacity and the ergodic secrecy capacity are obtained, providing insights into the impact of the Eve’s location uncertainty and the RIS design on the secrecy performance. Moreover, based on the derived CDFs for received SNRs at Eves, the secrecy outage probabilities are, respectively, analyzed. Specifically, under the constraint of the secrecy outage probability, the closed forms of the minimum required SNRs at Bob and the number of RIS elements are also obtained. Simulation and analytical results corroborate the derived expressions and reveal the tradeoff between the system’s energy efficiency and the number of RIS elements.