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.