Security analysis of the “Ping-Pong” quantum communication protocol in the presence of collective-rotation noise

Environmental noise is inevitable in non-isolated systems. It is, therefore, necessary to analyze the security of the “Ping-Pong” protocol in a noisy environment. An excellent model for collective-rotation noise is introduced, and information theoretical methods are applied to analyze the security of this protocol. If noise level ε is lower than 11%, an eavesdropper can gain some, but not all, information freely without being detected. Otherwise, the protocol becomes insecure. We conclude that the use of 'Ping-Pong' protocol as a quantum secure direct communication (QSDC) protocol is quasi-secure, as declared by the original author when ε⩽11%.