Bidirectional Controlled Simultaneous Quantum Teleportation within a Quantum Network Via Nine-Qubit Entangled State

This paper proposes a new bidirectional controlled simultaneous quantum teleportation protocol within a quantum network, which utilizes a nine-qubit entangled state as the quantum channel. In our protocol, Alice, Bob and Charlie can be both senders and receivers. Furthermore, we introduce a supervisor named David. Under the supervision of David, the transmission process is divided into two main scenarios: two senders & one receiver and one sender & two receivers. Before the transmission starts, we preprocess the transmitted entangled states using controlled-NOT gates. At this point, The entire transmission process needs to perform one measurement with the sixteen-mutually orthogonal four-qubit states, one simultaneous Bell-state measurement, and one single-qubit X basis measurement. Based on the measurement results, the communicators perform specific unitary operations and controlled-NOT operations to recover the initial states of the transmission. This protocol extends unidirectional simultaneous transmission to bidirectional simultaneous transmission for the first time, and it has significant advantages in terms of transmission efficiency.