Hierarchical controlled bidirectional hybrid quantum information transmission for arbitrary two-qubit states in noisy environments

This paper proposes a hierarchical controlled bidirectional hybrid quantum information transmission (HCBHQIT) protocol for arbitrary two-qubit states based on a special ten-qubit entangled state. The protocol implements a hierarchical control mechanism where high-level agent Alice can complete quantum teleportation of any unknown two-qubit state to Bob with only one controller Charlie's assistance, while low-level agent Bob requires collaborative control from both Charlie and an additional controller David to remotely prepare arbitrary known two-qubit states at Alice's location (with Alice remaining completely unaware of the state). We comprehensively analyze protocol implementation in noisy environments, particularly examining fidelity degradation under various noise conditions, and calculate the intrinsic efficiency through comparative evaluations. The scheme innovatively integrates multi-level control architecture with bidirectional hybrid communication technology over a shared quantum channel, with detailed discussions for both ideal and noisy scenarios. Demonstrated to maintain practical value across multiple application scenarios, this protocol advances controllable quantum communication systems through its hierarchical access management and dual-directional information transfer capabilities.