Fault tolerant practical quantum digital signature against collective noises

Quantum digital signature (QDS) has been proved to be secure in theory, but will inevitably be interfered by channel noise during the practice transmission of qubits. We propose two practical fault tolerant quantum digital signature protocols for the collective noises. For resisting the collective noises, a decoherence-free subspace (DFS) containing four logical qubits has been constructed, which improves the performance of QDS protocols in terms of communication fidelity. Moreover, we prove that the protocols are secure against forging and repudiation attacks, and further discuss the influence of different verification thresholds on the security and give a quantitative analysis.