Controlled quantum teleportation of a four-qubit cluster state using a seven-qubit entangled state in a noisy environment

Abstract

In this work, an efficient controlled quantum teleportation scheme was developed for the transmission of a four-qubit cluster state. The proposed approach relied on a seven-qubit entangled state as the quantum channel, enabling deterministic reconstruction of the quantum state through three-qubit and single-qubit projective measurements followed by corresponding unitary operations. Beyond the ideal scenario, the scheme’s robustness was evaluated by quantifying fidelity dynamics under bit-flip, phase-damping, and amplitude-damping decoherence channels, revealing a pronounced asymmetry: the protocol is highly vulnerable to bit-flip errors (\(f=0.4856\) at \(p=0.1\)), exhibits strong robustness against phase-damping noise (\(f=0.7824\)), and shows intermediate, state-dependent behavior under amplitude-damping noise (\(f=0.7053\) for balanced amplitudes). Compared with existing multi-party teleportation frameworks, the present scheme offers a more resource-efficient architecture with enhanced intrinsic operational efficiency. The proposed approach offers an effective solution for supervised information transfer in noisy quantum networking systems.