The quantum digital signature (QDS) has attracted much attention as it ensures the nonrepudiation, unforgeability, and transferability of signature messages based on information-theoretic security. Amiri et al. (Phys. Rev. A 93 032325) proposed the first practical QDS protocol based on orthogonal coding, which has realized information-theoretic security and become the mainstream paradigm in QDS research. The procedure of QDS involves two essential stages, the one is the distribution stage, in which Alice-Bob and Alice-Charlie individually utilize the three-intensity decoy-state quantum key distribution protocol but without error correction or privacy amplification, namely, key-generation protocol, to generate correlated bit strings, the other is the messaging stage, in which Alice transmits signature messages to the two recipients.

However, previous theoretical and experimental studies both overlooked the modulation errors that may be introduced in the state preparation process due to the imperfections in modulator devices. Under the traditional framework of GLLP analysis method, these errors will significantly reduce the actual signature rates. Therefore, we propose a state-preparation-error tolerant QDS and use parameter analysis to characterize the state preparation error to make the simulation analysis more realistic. In addition, we analyze the signature rates of the present scheme by using the three-intensity decoy-state method.

Compared with previous QDS protocols, our protocol almost shows no performance degradation under practical state preparation errors and exhibits a maximum transmission distance around 180 km. Furthermore, state preparation errors do not have a significant influence on the bit error rate induced by normal communication between the legitimate users or the one produced by an eavesdropper. These results prove that the method proposed in this paper has excellent robustness against state preparation errors and it can achieve much higher signature rates and signature distances than other standard methods. Besides, signature rates are basically unchanged under different total pulse numbers, which shows that our protocol also has good robustness against the finite-size effect. Additionally, in the key generation process, our method is only required to prepare three quantum states, which will reduce the difficulty of experiment realizations.

Furthermore, the proposed method can also be combined with the measurement-device-independent QDS protocol and the twin-field QDS protocol to further increase the security level of QDS protocol. Therefore, our work will provide an important reference value for realizing the practical application of QDS in the future.