We address the efficiencies of \((N+2)\)-qubit partially entangled states for the involvement of N controllers in a noisy environment from the perspective of controller’s authority and average fidelity of a controlled teleportation protocol. For this, we design a generalized circuit using single- and two-qubit gates and study different cases of two sets of partially entangled multiqubit states. The analysis shows that for a particular set of partially entangled \((N+2)\)-qubit states average fidelity is independent of the state parameter and measurements performed by \(N-1\) controllers in ideal conditions and measurements performed by \(N-1\) controllers in noisy conditions with or without applications of weak measurements and its reversal operations. The results thus facilitate the experimental setups to worry about less number of parameters in the protocol. We further compare the efficiencies of these states from a controller’s perspective to increase his/her authority in the protocol. In addition, we also analyze dense coding protocol with and without the involvement of controllers to demonstrate the usefulness of partially entangled states.

从控制器的权限和受控传送协议的平均保真度的角度，我们解决了噪声环境中N个控制器参与\（（N + 2）\）- qubit部分纠缠状态的效率。为此，我们设计了一个使用单量子比特和两个量子比特的门的通用电路，并研究了两组部分纠缠的多量子比特状态的不同情况。分析表明，对于一组特定的部分（\（（N + 2）\）- qubit纠缠态，平均保真度独立于状态参数和\（N-1 \）控制器在理想条件下执行的测量以及\（N-1 \）嘈杂条件下的控制器，无论是否应用弱测量及其反转操作。因此，结果便于实验设置担心协议中的参数数量较少。我们从控制器的角度进一步比较了这些状态的效率，以增加其在协议中的权限。此外，我们还分析了有无控制器的情况下的密集编码协议，以证明部分纠缠状态的有用性。