Fault tolerant two-step quantum secure direct communication protocol against collective noises

This work proposes two fault tolerant quantum secure direct communication (QSDC) protocols which are robust against two kinds of collective noises: the collective-dephasing noises and the collective-rotation noises, respectively. The two QSDC protocols are constructed from four-qubit DF states which consist of two logical qubits. The receiver simply performs two Bell state measurements (rather than four-qubit joint measurements) to obtain the secret message. The protocols have qubit effciency twice that of the other corresponding fault tolerant QSDC protocols. Furthermore, the proposed protocols are free from Trojan horse attacks.