The bidirectional quantum digital signature with enhanced performance

Communication distance and signature length are important performance indicators to evaluate quantum digital signatures (QDS), as they directly affect the practicality and scalability of the protocol. Either extending the communication distance or reducing the signature length can both effectively promote the practical deployment of QDS. In this study, two example steps from the bidirectional entanglement purification protocol, namely Step B and Step P, are applied to the QDS protocol, proposing bidirectional communication quantum digital signature (BD-QDS). The comparative analysis of four different combinations of Step B and Step P is presented to explore their respective effects on QDS performance. Numerical simulation results demonstrate that adopting Step B in the QDS protocol can extend the communication distance, while adopting Step P can reduce the signature length. A key observation is that applying Step B followed by Step P achieves a greater performance improvement in QDS than using either Step B or Step P individually. This paper proposes the BP-BD-QDS protocol, which not only extends the communication distance but also reduces the signature length.