Sending or not sending twin-field quantum key distribution with distinguishable decoy states

Abstract: Twin-field quantum key distribution (TF-QKD) and its variants can overcome the fundamental rate-distance limit of QKD which has been demonstrated in the laboratory and field while their physical implementations with side channels remains to be further researched. We find the external modulation of different intensity states through the test, required in those TF-QKD with post-phase compensation, shows a side channel in frequency domain. Based on this, we propose a complete and undetected eavesdropping attack, named passive frequency shift attack, on sending or not-sending (SNS) TF-QKD protocol given any difference between signal and decoy states in frequency domain which can be extended to other imperfections with distinguishable decoy states. We analyze this attack by giving the formula of upper bound of real secure key rate and comparing it with lower bound of secret key rate under Alice and Bob's estimation with the consideration of actively odd-parity pairing (AOPP) method and finite key effects. The simulation results show that Eve can get full information about the secret key bits without being detected at long distance. Our results emphasize the importance of practical security at source and might provide a valuable reference for the practical implementation of TF-QKD.