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Quantum entanglement is a fundamental physical resource that enables a range of information-processing tasks with no efficient solution on classical computers. In this paper, we construct a class of general maximum entangled states by parameterizing the coefficients of Bell states. By calculating, we obtain the local unitary operations required to realize the mutual transformation of the constructed states, analogous to Pauli operators acting on one particle of a Bell state. Interestingly, the local unitary operations on the two particles of Bell states are identical, whereas for the constructed states, they must differ in certain cases. To explore the potential applications of these maximum entangled states and the obtained local unitary operations, we design a class of measurement-device-independent quantum secure direct communication protocols based on entanglement swapping. In the class of designed protocols, entanglement swapping is realized between a constructed maximum entangled state and a Bell state. We demonstrate that the class of designed protocols have no information leakage and can resist intercept-and-resend attacks, measure-resend attacks, and collective attacks. In addition, the unconditional security of the class of designed protocols is proved. We believe that the constructed maximum entangled states and the obtained local unitary operations may find applications in other quantum information-processing fields.
Liu et al. (Thu,) studied this question.