Fault-tolerant Semiquantum key Distribution Over a Collective-dephasing Noise Channel

Semiquantum key distribution (SQKD) allows two remote users, quantum Alice and classical Bob, to share a secret key via a quantum channel and an authenticated classical channel. In most of the existing SQKD protocols, SQKD is possible only under the assumption of ideal quantum channels. However, the noise in quantum channels is unavoidable. In this paper, we propose two fault-tolerant SQKD protocols, the randomization-based SQKD protocol and the measure-resend SQKD protocol, which are robust against the collective-dephasing noise. Logical qubits have been selected to build travelling blocks for constructing a decoherence-free subspace (DFS). Compared with the previous SQKD protocols, our protocols can provide higher communication fidelity. In addition, a security proof is given in the subsequent section.