Fault tolerant authenticated quantum direct communication immune to collective noises

This study proposes two new coding functions for GHZ states and GHZ-like states, respectively. Based on these coding functions, two fault tolerant authenticated quantum direct communication (AQDC) protocols are proposed. Each of which is robust under one kind of collective noises: collective-dephasing noise and collective-rotation noise, respectively. Moreover, the proposed AQDC protocols enable a sender to send a secure as well as authenticated message to a receiver within only one step quantum transmission without using the classical channels.