Experimental Mode-Pairing Quantum Key Distribution Surpassing the Repeaterless Bound
Likang Zhang, Wei Li, Jiawei Pan, Yichen Lu, Wenwen Li, Zheng-Ping Li, Yizhi Huang, Xiongfeng Ma, Feihu Xu, Jian-Wei Pan
Abstract
Quantum key distribution (QKD) provides information-theoretic security for communication. The mode-pairing (MP) protocol emerges as a promising solution for long-distance QKD by eliminating the need for a global phase reference while maintaining the repeaterlike rate-loss scaling. Recent implementations have demonstrated its potential, but they either rely on costly ultrastable lasers or struggle with phase fluctuations from commercial lasers, particularly over long distances. As a result, surpassing the repeaterless bound with a practical system remains a challenge. In this work, we demonstrate a practical high-performance MP-QKD system using commercial lasers. To address phase fluctuations, we propose a frequency-tracking scheme based on fast Fourier transformation, enabling us to extend the pairing length to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>2</a:mn> <a:mo>×</a:mo> <a:msup> <a:mn>10</a:mn> <a:mn>5</a:mn> </a:msup> </a:math> pulses ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>160</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi mathvariant="normal">μ</c:mi> <c:mi mathvariant="normal">s</c:mi> </c:mrow> </c:math> ). We propose a model to carefully analyze the phase noise and optimize the system parameters. Our system achieves an optimal secret key rate of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mn>47.8</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>bit</g:mi> <g:mo>/</g:mo> <g:mi mathvariant="normal">s</g:mi> </g:mrow> </g:math> over 403 km of standard fiber (76.5 dB loss), exceeding the repeaterless bound by a factor of 2.92. Furthermore, we compare MP-QKD and twin-field QKD under various practical conditions and clarify the distinct application scenarios of the two protocols. These results confirm the feasibility of MP-QKD using cost-effective commercial technologies, paving the way for scalable quantum communication networks.