Scalable High-Rate Twin-Field Quantum Key Distribution Networks without Constraint of Probability and Intensity

Implementation of a twin-field quantum key distribution network faces limitations, including the low tolerance of interference errors for phase-matching type protocols and the strict constraint regarding intensity and probability for sending-or-not-sending type protocols. Here, we propose a two-photon twin-field quantum key distribution protocol inspired by multiplexing in quantum repeaters. We achieve twin-field-type two-photon interference through post-matching phase-correlated single-photon interference events. We exploit the non-interference mode as the code mode to highly tolerate interference errors, and the two-photon interference naturally removes the intensity and probability constraint. Therefore, our protocol can transcend the abovementioned limitations while breaking the secret key capacity of repeaterless quantum key distribution. These features are tailored for scalable quantum networks, under which each node with fixed system parameters can dynamically switch different attenuation links. Simulations show that for a four-user network, the key rates of our protocol for all six links can either exceed or approach the secret key capacity. However, the key rates of all links are lower than the key capacity when using phase-matching type protocols. Additionally, four of the links could not extract the key when using sending-or-not-sending type protocols. We anticipate that our protocol can facilitate the development of practical and efficient quantum networks.