In 2006, Xue et al. [Chin. Phys. 15, 1421] proposed a dense coding on the symmetric W state |W〉=1/√13(|001〉+|010〉+|100〉) to establish a deterministic quantum communication (DQC) protocol. In the dense coding, however, the encoded message can be recovered with a 67% probability. Therefore, within one execution of their protocol, the sender can only successfully transmit 67% of information to the receiver. The same protocol has to be repeated several times before a message is fully transmitted. The purpose of this study is to propose a novel coding function of the symmetric W state for constructing a DQC protocol which can fully transmit the message within one execution of DQC. Furthermore, the security of the protocol is analyzed to show that any eavesdropper will be detected with a very high probability if he/she attempts to steal any information.
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