Three-party reference frame independent quantum key distribution protocol

We present a three-party reference frame independent quantum key distribution protocol which can be implemented without any alignment of reference frames between the sender and the receiver. The protocol exploits entangled states to establish a secret key among three communicating parties. We derive the asymptotic key rate for the proposed protocol against collective attacks and perform a finite-size key security analysis against general attacks in the presence of statistical fluctuations. We investigate the impact of reference frame misalignment on the stability of our protocol, and we obtain a transmission distance of 180 km, 200 km, and 230 km for rotation of reference frames β=π/6, β=π/8 and β=0, respectively. Remarkably, our results demonstrate that our proposed protocol is not heavily affected by an increase in misalignment of reference frames as the achievable transmission distances are still comparable to the case where there is no misalignment in reference frames (when β=0). We also simulate the performance of our protocol for a fixed number of signals. Our results demonstrate that the protocol can achieve an effective key generation rate over a transmission distance of about 120 km with realistic 10⁷ finite data signals and approximately achieve 195 km with 10⁹ signals. Moreover, our proposed protocol is robust against noise in the quantum channel and achieves a threshold error rate of 22.7%.