Bidirectional cyclic hybrid quantum information transmission of arbitrary single-qubit state with different levels of control

Current hierarchical control quantum communication protocols are mostly limited to linear bidirectional architectures with only two communication agents, lacking cyclic information exchange capabilities and flexible scalability for large-scale scenarios. This limitation impedes the practical deployment of complex quantum communication networks. To address this issue, a novel hierarchical control bidirectional cyclic hybrid quantum information transmission protocol for an arbitrary single-qubit state is proposed. The protocol comprises six participating entities: three communication agents (Alice, Bob, and Charlie) at different levels and three control agents (David, Emma, and Frank) with a clear permission hierarchy. The bidirectional communication tasks of each communication agent require matching control authorization corresponding to their level: high-level communication agents only need David's assistance, mid-level ones require joint control from David and Emma, and low-level ones demand collaborative authorization from all three control agents to complete their quantum teleportation and remote state preparation tasks. Furthermore, the proposed six-party protocol is extended to a 2N-party scenario involving N control agents and N communication agents at different levels, adapting to the needs of large-scale quantum communication networks. This work provides a flexible and scalable theoretical framework for constructing hierarchical quantum communication networks with cyclic information exchange.