Experimental Efficient Source-Independent Quantum Conference Key Agreement

TL;DR

This work tackles the challenge of scalable, source-independent multi-user quantum conference key agreement by implementing a tripartite SI-QCKA based on Bell-state distribution with a post-matching method to generate GHZ correlations in a three-user star network. The authors demonstrate high-quality entanglement (fidelities near $97\%$ and visibilities above $96\%$) and substantial secure key rates, achieving up to $2.11 \times 10^{4}$ bit/s at a channel transmission of $1.64 \times 10^{-1}$ with $p_z=0.9$, while exploring the impact of channel loss and basis probabilities across six configurations. The approach eliminates the need for multipartite entangled-state generation, offering a scalable and efficient pathway for future large-scale quantum networks and potential integration with dense wavelength-division multiplexing in fully connected QKD networks. Overall, the results establish a practical route to secure multi-user quantum communication leveraging source-independence and Bell-state distribution with post-processing, paving the way for robust quantum network architectures.

Abstract

Multipartite entanglement enables secure group key distribution among multiple users while providing immunity against hacking attacks targeting source devices, thereby realizing source-independent quantum conference key agreement (SI-QCKA). However, previous experimental demonstrations of SI-QCKA have encountered substantial technical challenges, primarily due to the low efficiency and scalability limitations inherent in the generation and distribution of multipartite entanglement. Here, we experimentally demonstrate a scalable and efficient SI-QCKA protocol using polarization-entangled photon pairs in a three-user star network, where Greenberger-Horne-Zeilinger correlations are realized via a post-matching method. We achieve a secure group key rate of $2.11 \times 10^{4}$ bits/s under the single-user channel transmission of 1.64 $\times$ $10^{-1}$ in a symmetric channel loss network. Additionally, we conduct six sets of experiments to investigate the impact of varying channel transmission and random basis selection probabilities on secure key rates. Our work establishes an efficient pathway for SI-QCKA and demonstrates potential scalability for future large-scale multi-user quantum networks.

Figures (3)

• Figure 2: Schematic of the QCKA experimental setup. (a) Sagnac loops. Laser pulses centered at a wavelength of 780 nm are injected into Sagnac loops, where polarization-entangled photon pairs at a wavelength of 1560 nm are generated via type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (PPKTP) crystal. The half wave plates (HWPs) in the Sagnac loops are operational at both 780 nm and 1560 nm wavelengths. Entangled photon pairs are sequentially allocated to Alice, $\text{Bob}_1$ and $\text{Bob}_2$ for polarization projection measurements. (b), (c) and (d) The single-photon polarization measurements of the users. In the measurement sites, beam splitters (BSs) are utilized for random basis selection. The HWPs following the BS cooperate with the polarizing beam splitter (PBS) to perform projection measurements. The HWPs are set at $0^\circ$/$45^\circ$ and $22.5^\circ$/$67.5^\circ$ for measurements in the horizontal/vertical (H/V) and diagonal/anti-diagonal (D/A) bases, respectively. Photons are then measured in different bases and detected by distinct SNSPDs. QWP, quarter-wave plate; DM, dichroic mirror.
• Figure 3: The characterization parameters of the two entangled photon pairs. (a)-(c) correspond to Alice and $\text{Bob}_1$, and (d)-(f) correspond to Alice and $\text{Bob}_2$. (a) and (d) Two-photon interference fringes as functions of the polarizer angles of Alice and $\text{Bob}_1$ (or $\text{Bob}_2$) under two different phase bases. Alice sets $\theta_A$ to $0^{\circ}$ (green points, fitted with green line) and $45^{\circ}$ (magenta points, fitted with magenta line), while $\text{Bob}_i$ sweeps $\theta_{B_i}$ from $0^{\circ}$ to $180^{\circ}$. (b) and (e) Quantum state tomography results. The real and imaginary parts of the density matrix are depicted with respect to $\ket{\Psi^-} = (\ket{HV}-\ket{VH})/\sqrt{2}$. (c) and (f) The four expectation values used to calculate the S parameter of the CHSH inequality. (c) $E_{AB_1}(0^{\circ},-22.5^{\circ}) = -0.631 \pm 0.004$, $E_{AB_1}(0^{\circ},22.5^{\circ}) = -0.733 \pm 0.003$, $E_{AB_1}(-45^{\circ},-22.5^{\circ}) = -0.723 \pm 0.003$, $E_{AB_1}(-45^{\circ},22.5^{\circ}) = 0.627 \pm 0.004$. (f) $E_{AB_2}(0^{\circ},-22.5^{\circ}) = -0.708 \pm 0.003$, $E_{AB_2}(0^{\circ},22.5^{\circ}) = -0.700 \pm 0.003$, $E_{AB_2}(-45^{\circ},-22.5^{\circ}) = -0.647 \pm 0.003$, $E_{AB_2}(-45^{\circ},22.5^{\circ}) = 0.666 \pm 0.003$.
• Figure 4: Conference secure key rate as a function of channel transmission $\eta$. The five-pointed blue stars and red triangles represent the experimental results for $p_z = 0.9$ and $p_z = 0.5$, respectively. For each $p_z$, the QCKA key rates are measured under three different channel transmission values, where the channel transmission $\eta$ denotes the transmission from the central node to each user. The blue and red lines represent the simulation results for $p_z = 0.9$ and $p_z = 0.5$, respectively.