  Two fault tolerant authenticated quantum dialogue (AQD) protocols are
proposed in this paper by employing logical Bell states as the quantum
resource, which combat the collective-dephasing noise and the
collective-rotation noise, respectively. The two proposed protocols each can
accomplish the mutual identity authentication and the dialogue between two
participants simultaneously and securely over one kind of collective noise
channels. In each of two proposed protocols, the information transmitted
through the classical channel is assumed to be eavesdroppable and modifiable.
The key for choosing the measurement bases of sample logical qubits is
pre-shared privately between two participants. The Bell state measurements
rather than the four-qubit joint measurements are adopted for decoding. The two
participants share the initial states of message logical Bell states with
resort to the direct transmission of auxiliary logical Bell states so that the
information leakage problem is avoided. The impersonation attack, the
man-in-the-middle attack, the modification attack and the Trojan horse attacks
from Eve all are detectable.
