A universal protocol for controlled bidirectional quantum state transmission

In this paper, we propose a universal protocol for controlled bidirectional quantum state transmission. The bidirectional transmission of n1- and n2-qubit equatorial states can be realized by using the 2n1+2n2+1-qubit entangled state as the quantum channel, where n1,n2 are arbitrary nonzero positive integers. First, the quantum channel is constructed by using Hadamard (H) and CNOT operations. Furthermore, after the protocol completed, the desired state can be obtained simultaneously, securely and determinately. Second, two examples are given. One is a symmetric protocol which can complete the bidirectional transmission of two-qubit equatorial state. The other is an asymmetric protocol, where Alice transmits a single-qubit equatorial state to Bob and Bob transmits a four-qubit equatorial state to Alice. To the best of our knowledge, it is the first time to realize the bidirectional transmission of arbitrary-qubit equatorial state. At last, we analyze the performance of the protocol. Some comparisons with other protocols are described.