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

Quantum secure direct communication is one of the major branches of quantum cryptography, which sends secret information through a quantum channel directly without setting up a prior key. Over the past decade, numerous protocols have been proposed, and some of them have been experimentally demonstrated. The two-way protocol is seen as one of the most practical protocol; in this paper, we present the security proof of the two-way quantum secure direct communication protocol when the noisy and lossy channel is taken into account.