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Non-Orthogonal Multiple Access-Based Continuous-Variable Quantum Key Distribution: Secret Key Rate Analysis and Power Allocation

Zhichao Dong, Xiaolin Zhou, Huang Peng, Wei Ni, Ekram Hossain, Xin Wang

TL;DR

This paper addresses secure multi-user CVQKD for a large-scale quantum Internet under collective attacks. It proposes an uplink NOMA-CVQKD architecture with a SIC-based heterodyne receiver to enable simultaneous transmissions from $K$ users. It derives asymptotic lower bounds for user SKRs via the entropy power inequality and maximum entropy principle, and asymptotic upper bounds on Eve’s information via the Holevo quantity, yielding an asymptotic sum SKR $\tilde{I}_{sum}^{(sec)}$. A successive convex approximation (SCA) based power allocation algorithm is developed with guaranteed convergence to a local KKT point, and simulations show up to 23% sum SKR gain over Q-OMA with up to 16 users under turbulence and varying distances. These results demonstrate scalable, turbulence-robust CVQKD in multi-user networks with practical power constraints.

Abstract

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.

Non-Orthogonal Multiple Access-Based Continuous-Variable Quantum Key Distribution: Secret Key Rate Analysis and Power Allocation

TL;DR

This paper addresses secure multi-user CVQKD for a large-scale quantum Internet under collective attacks. It proposes an uplink NOMA-CVQKD architecture with a SIC-based heterodyne receiver to enable simultaneous transmissions from users. It derives asymptotic lower bounds for user SKRs via the entropy power inequality and maximum entropy principle, and asymptotic upper bounds on Eve’s information via the Holevo quantity, yielding an asymptotic sum SKR . A successive convex approximation (SCA) based power allocation algorithm is developed with guaranteed convergence to a local KKT point, and simulations show up to 23% sum SKR gain over Q-OMA with up to 16 users under turbulence and varying distances. These results demonstrate scalable, turbulence-robust CVQKD in multi-user networks with practical power constraints.

Abstract

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.

Paper Structure

This paper contains 35 sections, 4 theorems, 57 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Quantum OMA
  4. Quantum NOMA
  5. Collective Attack
  6. Contributions
  7. System Model and Assumptions
  8. Transmitters/Users
  9. Receiver/BS
  10. Attack Model
  11. Intercepted Quantum Information
  12. Quantum State Storage and Optimal Quantum Measurement
  13. Reverse Reconciliation
  14. Analysis of SKR for Uplink NOMA-CVQKD
  15. Lowe-Bound for the Key Rate Under Collective Attack
  16. ...and 20 more sections

Key Result

Lemma 1

The sum-rate of the uplink NOMA-CVQKD system is given by where $\mathrm{Pr}\left( Y|\boldsymbol{X} \right)$ is given in eq:basePr_group, and gives the joint PDF of the independent Gaussian-modulated quadratures $\boldsymbol{X} = [X_1, \dots, X_K]^T$, with variance $V_{a}^{(k)}$ per $X_k$, $\forall k$. Moreover, $I_{\text{sum}}$ converges, as $\|\boldsymbol{X}\|\to\infty$ and $|y|\to\infty$.

Figures (8)

  • Figure 1: An illustration of the considered uplink NOMA-CVQKD system where $K$ users form an uplink NOMA cluster, with each user transmitting key using Gaussian-modulated coherent states. The BS employs an SIC-based heterodyne receiver to sequentially detect the received coherent states, while Eve performs a collective attack to extract the secret key during the CVQKD process.
  • Figure 2: Comparison of sum SKR between Algorithms 1, Q-OMA, UQPA, and CIH under 16 users.
  • Figure 3: Comparison of sum SKR under different atmospheric turbulence scenarios, where there are 8 users.
  • Figure 4: Sun SKR for different received power and channel transmittance.
  • Figure 5: Sun SKR for different excess noises and channel transmittance.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof
  • Theorem 2