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Quantum key distribution (QKD),which aims to establish an unconditionally secure secret key between two remote authorized users through the transmission of quantum signals,has been one of the most important applications of quantum mechanics.Since the well-known BB84 protocol was proposed by Bennett and Brassard[1] in 1984,many good QKD protocols[2-4] have been proposed.In recent years,the new concept of quantum secure direct communication (QSDC) has been put forward.Different from OKD,QSDC allows secret messages to be communicated directly without creating a key to encrypt them in advance.Since the well-known Ping-Pong protocol was proposed by Bostrom and Felbinger[5] in 2002,many good QSDC protocols[6-9] have been put forward.However,these protocols are one-way communication protocols.Fortunately,the concept of bidirectional QSDC was proposed by Nguyen[10] in 2004,where two remote users are able to exchange their secret messages simultaneously.