Continuous-variable quantum key distribution network based on entangled states of optical frequency combs

TL;DR

This work tackles scalable multi-user CVQKD by leveraging entangled optical frequency combs generated with a type-II OPO and employing entanglement-in-the-middle to enable simultaneous, fully connected key distribution. The authors detail a star-network architecture with a central node distributing comb-tooth EPR pairs to users, using LO distribution and wavelength-division multiplexing to support many users. They derive the TMSS covariance matrix and a secret-key rate $K = \beta I_{AB} - \chi_{AE}$ in the asymptotic regime, accounting for seed-laser excess noise and OPO cavity-length jitter, and validate feasibility through simulations showing short-distance viability under controlled loss/noise. The study identifies intracavity loss and optical-component insertions as the main practical bottlenecks, offering design directions toward reducing losses to enable scalable, high-rate quantum networks based on optical frequency combs.

Abstract

Continuous-variable quantum key distribution (CVQKD) features a high key rate and compatibility with classical optical communication. Developing expandable and efficient CVQKD networks will promote the deployment of large-scale quantum communication networks in the future. This paper proposes a CVQKD network based on the entangled states of an optical frequency comb. This scheme generates Einstein-Podolsky-Rosen entangled states with a frequency comb structure through the process of a type-II optical parametric oscillator. By combining with the scheme of entanglement in the middle, a fully connected CVQKD network capable of distributing secret keys simultaneously can be formed. We analyze the security of the system in the asymptotic case. Simulation results show that under commendable controlling of system loss and noise, the proposed scheme is feasible for deploying a short-distance fully connected CVQKD network. Loss will be the main factor limiting the system's performance. The proposed scheme provides new ideas for a multi-user fully connected CVQKD network.

Figures (5)

• Figure 1: Schematic of the optical frequency comb entanglement state based CVQKD networks. $\pm n$s(i) represents the signal (idler) comb with frequency of $\omega_0 \pm n\Omega$. NOPA, nondegenerate optical parametric amplifier; BS, beamsplitter; AM, amplitude modulator; DBS, dichroic beamsplitter; PBS, polarization beamsplitter; PC, polarization controller; MC, mode cleaner; WS, waveshaper; MZM, Mach-Zehnder Modulator; Het, heterodyne detection.
• Figure 2: Schematic of the optical frequency comb entanglement state based 4 users CVQKD networks. $\pm n$s(i) represents the signal (idler) comb with frequency of $\omega_0 \pm n\Omega$, where $n = 1,2,3$.
• Figure 3: The noise contributed from the extra optical noise carried by the seed and fluctuations of the length of the OPO cavity as a function of the frequency. (a) The noise introduced by the seed optical noise to the generated TMSS. (b) The noise introduced by fluctuations of the length of the OPO cavity to the generated TMSS. (c) The covariance noise $\tilde{C} _N^{in,x/p}$ introduced by the seed optical noise to the generated TMSS. (d) The covariance noise $\tilde{C} _{\delta\Delta}^{xp/px}$ introduced by the seed optical noise to the generated TMSS.
• Figure 4: The asymptotical security of the proposed scheme between any two arbitrary users under different OPO parameters. (a) The secret key rate as a function of the transmittance distance for the proposed scheme under different total decay rate $T_{tot}$ of the NOPA. (b) The secret key rate as a function of the transmittance distance for the proposed scheme under different single-pass parametric gain amplitude $\chi$. (c) The secret key rate as a function of the transmittance distance for the proposed scheme under different attenuations $\eta_1$ and $\eta_2$ of the center node. (d) The secret key rate as a function of the transmittance distance for the proposed scheme under different detector parameters.
• Figure 5: The asymptotical security of the proposed scheme between arbitrary two users under different settings of the system's parameters. (a) The secret key rate as a function of the transmittance distance for the proposed scheme under different values of insertion loss $\eta_1$ and $\eta_2$ of the optical elements in the center node. (b) The secret key rate as a function of the transmittance distance for the proposed scheme under different values of excess noise. (c) The secret key rate as a function of the transmittance distance for the proposed scheme under different detector parameters. (d) The secret key rate as a function of the transmittance distance for the proposed scheme under different reconciliation efficiencies.