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Quantum secure direct communication is one of the important mode of quantumcommunication, which sends secret information through a quantum channeldirectly without setting up a prior key. Over the past decade, numerousprotocols have been proposed, and part of them have been experimentallydemonstrated. However, the strict security proof is still in suspense. Two-wayprotocol is seen as one of the most practical protocol, in this paper, thesecurity of the two-way quantum secure direct communication protocol will beproved against general attacks when the noisy and lossy channel is taken intoaccount. There are two steps included in the proof, firstly, we need to provethat the mutual information between Alice and Bob is larger than the mutualinformation shared between Alice and the eavesdropper when the error rate incontrol mode is less than the predetermined threshold. Secondly, once the errorrate is lower than the threshold, one can always find out a forward errorcorrection code to guarantee the security of information transmission.

Security proof of the two-way quantum secure direct communication with channel loss and noise