Assisted quantum teleportation

Teleportation through a non-maximally entangled pair, e.g., $\ket{\psi(\theta)}_{AB}=\cos\theta\ket{00}+\sin\theta\ket{11}$, induces a noisy channel and cannot achieve deterministic unit-fidelity transmission unless $\theta=\pi/4$. We introduce a framework of \emph{assisted quantum teleportation} in which a third party (the ``Bank'') supplies auxiliary multipartite entanglement to restore a perfect Bell pair on the original $AB$ registers. We analyze two operational roles for the Bank: a Bank-measures model (measurement and broadcast) and a transfer model (the Bank transfers its subsystem and then leaves). For GHZ-class and W-class assistance we derive explicit feasibility regions for deterministic restoration and show an operational inequivalence for W resources. We further characterize finite-shot optimal success probabilities for probabilistic restoration and formulate Bank-measures feasibility for general pure Bank resources as a minimax optimization.