Quantum secure direct dialogue over collective noise channels based on logical Bell states

A scheme for quantum secure direct dialogue protocols, which is adapted to both collective-dephasing noise and collective-rotation noise, is proposed in this paper by using the logical Bell states as the traveling states to resist collective noise. All logical Bell states are used to transmit secret messages from either of two participants except those used for security checks. Each of the logical Bell states used for transmitting secret messages can carry two classical bits. Bell state measurements rather than four-qubit joint measurements are used for decoding. The two participants can accomplish the direct dialogue without any additional classical communication for decoding. The information leakage problem is avoided with resort to the two-step transmission, the ping-pong transmission and the absence of classical communication for the encoded quantum states. The two participants can speak to each other either simultaneously or sequentially. Furthermore, the two participants can transmit secret messages of different lengths to each other in one round communication. The proposed scheme is so flexible that it is much alike the practical conversation in real life.