Abstract
We first put forward an efficient protocol in ideal environment to deterministically realize bidirectional hybrid quantum communication via a five-qubit entangled state as the quantum channel, where both the senders transfer an arbitrary single-qubit state to each other simultaneously with the assistance of the controller. It is worth mentioning that three-bit classical communication can be saved at the broadcast channel by the technology of network coding. Moreover, the senders do not need to perform information splitting and additional unitary operations owing to the elaborate measurement basis we constructed. Then we investigate the protocol in five-type noises (the bit flip, phase flip, bit-phase flip, phase-damping and amplitude-damping noise) and calculate the corresponding fidelities of the output states.
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