We address the multi-user quantum key distribution (QKD) problem under malicious quantum attacks, which is critical for realizing a large-scale quantum Internet. This paper maximizes the sum secret key rate (SKR) of a novel uplink non-orthogonal multiple access based continuous-variable QKD (NOMA-CVQKD) system under collective attacks. The proposed system uses Gaussian-modulated coherent states and a quantum successive interference cancellation based heterodyne receiver. We derive closed-form asymptotic bounds for the legitimate users' achievable key rates via the entropy power inequality and maximum entropy principle, as well as for the eavesdropper's intercepted information based on Holevo information. A successive convex approximation based power allocation algorithm is developed to maximize the asymptotic sum SKR of the NOMA-CVQKD system under collective attacks, with guaranteed convergence to a locally optimal Karush-Kuhn-Tucker solution. Simulation results show that the proposed NOMA-CVQKD system with the power allocation algorithm achieves up to 23% higher sum SKR than quantum-orthogonal multiple access, supports 16 users at excess noise variance 0.1, and remains robust under varying turbulence intensities and transmission distances.
We address the multi-user quantum key distribution (QKD) problem under malicious quantum attacks, which is critical for realizing a large-scale quantum Internet. This paper maximizes the sum secret key rate (SKR) of a novel uplink non-orthogonal multiple access based continuous-variable QKD (NOMA-CVQKD) system under collective attacks. The proposed system uses Gaussian-modulated coherent states and a quantum successive interference cancellation based heterodyne receiver. We derive closed-form asymptotic bounds for the legitimate users' achievable key rates via the entropy power inequality and maximum entropy principle, as well as for the eavesdropper's intercepted information based on Holevo information. A successive convex approximation based power allocation algorithm is developed to maximize the asymptotic sum SKR of the NOMA-CVQKD system under collective attacks, with guaranteed convergence to a locally optimal Karush-Kuhn-Tucker solution. Simulation results show that the proposed NOMA-CVQKD system with the power allocation algorithm achieves up to 23% higher sum SKR than quantum-orthogonal multiple access, supports 16 users at excess noise variance 0.1, and remains robust under varying turbulence intensities and transmission distances.
Coherent states have been increasingly considered in optical quantum communications (OQCs). With the inherent non-orthogonality of coherent states, non-orthogonal multiple-access (NOMA) naturally lends itself to the implementation of multi-user OQC. However, this remains unexplored in the literature. This paper proposes a novel successive interference cancellation (SIC)-based Kennedy receiver for uplink NOMA-OQC systems, along with a new approach for power allocation of the coherent states emitted by users. The key idea is to rigorously derive the asymptotic sum-rate of the considered systems, taking into account the impact of atmospheric turbulence, background noise, and lossy photon channel. With the asymptotic sum-rate, we optimize the average number of photons (or powers) of the coherent states emitted by the users. Variable substitution and successive convex approximation (SCA) are employed to convexify and maximize the asymptotic sum-rate iteratively. A new coherent-state power allocation algorithm is developed for a small-to-medium number of users. We further develop its low-complexity variant using adaptive importance sampling, which is suitable for scenarios with a medium-to-large number of users. Simulations demonstrate that our algorithms significantly enhance the sum-rate of uplink NOMA-OQC systems using coherent states by over 20\%, compared to their alternatives.
Coherent states have been increasingly considered in optical quantum communications (OQCs).With the inherent non-orthogonality of coherent states, non-orthogonal multiple-access (NOMA) naturally lends itself to the implementation of multi-user OQC. However, this remains unexplored in the literature. This paper proposes a novel successive interference cancellation (SIC)-based photon-number-resolving detection (PNRD)-Kennedy receiver for uplink NOMA-OQC systems, along with a new approach for power allocation of the coherent states emitted by users. The key idea is to rigorously derive the asymptotic sum-rate of the considered systems, taking into account the impact of atmospheric turbulence, background noise, and lossy photon channel. With the asymptotic sum-rate, we optimize the average number of photons (or powers) of the coherent states emitted by the users. Variable substitution and successive convex approximation (SCA) are employed to convexify and maximize the asymptotic sum-rate iteratively. A new coherent-state power allocation algorithm is developed for a small-to-medium number of users. We further develop its low-complexity variant using adaptive importance sampling, which is suitable for scenarios with a medium-to-large number of users. Simulations demonstrate that our algorithms significantly enhance the sum-rate of uplink NOMA-OQC systems using coherent states by over 20%, compared to their alternatives.
Quantum key distribution (QKD), providing a way to generate secret keys with information-theoretic security, is arguably one of the most significant achievements in quantum information. The continuous-variable QKD (CV-QKD) offers the potential advantage of achieving a higher secret key rate (SKR) within a metro area, as well as being compatible with the mature telecom industry. However, the SKR and transmission distance of state-of-the-art CV-QKD systems are currently limited. Here, based on the proposed orthogonal-frequency-division-multiplexing (OFDM) CV-QKD protocol, we demonstrate a high-rate multi-carrier (MC) CV-QKD with a 10 GHz symbol rate that achieves Gbps SKR within 10 km and Mbps SKR over 100 km in the finite-size regime under composable security against collective attacks. The results are achieved by suitable optimization of subcarrier number and modulation variance, well-controlled excess noise induced by both the OFDM mechanism and the efficient DSP scheme, and high-performance post-processing capacity realized by the heterogeneous computing scheme. The composable finite-size SKR reaches 1779.45 Mbps@5 km, 1025.49 Mbps@10 km, 370.50 Mbps@25 km, 99.93 Mbps@50 km, 25.70 Mbps@75 km, and 2.25 Mbps@100 km, which improves the SKR by two orders of magnitude and quintuples the maximal transmission distance compared to the most recently reported CV-QKD results [ Nat. Commun. 13 , 4740 ( 2022 ) NCAOBW 2041-1723 10.1038/s41467-022-32161-y ]. Interestingly, it is experimentally verified that the SKR of the proposed MC CV-QKD can approach five times larger than that of the single-carrier CV-QKD with the same symbol rate without additional hardware costs. Our work constitutes a critical step toward future high-speed quantum metropolitan and access networks.
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.
Quantum wireless communications (QWC) is gaining much attention for its incomparable advantages of secure key transmission in free-space scenarios. In this paper, a novel iterative multi-user quantum key distribution (MQKD) non-orthogonal multiple-access (NOMA) system over Poisson atmospheric channels is proposed. Considering the atmospheric attenuation and quantum direct product operation, a MQKD parallel interference cancellation (PIC) approach is designed at the receiver. In particular, a quantum nonlinear Poisson shot noise limited sum-product interference cancellation algorithm is derived. Simulation results show that the proposed scheme is capable of mitigating the multi-user interference effectively, even considering the polarization mismatch. Quantitatively, for the 4-user scenario, it can achieve the classical Bit Error Rate (BER) of 3 x 10-6 at 2.5 km distance with polarization mismatch factor of 0.05. Moreover, the proposed NOMA-MQKD scheme can have obviously higher secure key rate than the conventional WDMA-MQKD approach.
We prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous-variable quantum key distribution (CVQKD). In a multicarrier CVQKD scenario, the Gaussian input quantum states of the legal parties are granulated into Gaussian subcarrier CVs (continuous-variables). The multicarrier communication formulates Gaussian sub-channels from the physical quantum channel, each dedicated to the transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitary CV operation, which results in the recovered single-carrier Gaussian CVs. We derive the formulas through the AMQD (adaptive multicarrier quadrature division) scheme, the SVD-assisted (singular value decomposition) AMQD, and the multiuser AMQD-MQA (multiuser quadrature allocation). We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison to single-carrier CVQKD. We derive the private classical capacity of a Gaussian sub-channel and the security parameters of an optimal Gaussian collective attack in the multicarrier setting. We reveal the secret key rate formulas for one-way and two-way multicarrier CVQKD protocols, assuming homodyne and heterodyne measurements and direct and reverse reconciliation. The results reveal the physical boundaries of physically allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the improved transmission rates lead to enhanced secret key rates and security thresholds.