Assisted quantum teleportation

TL;DR

This paper introduces a framework for assisted quantum teleportation where a third party supplies entanglement to enable perfect teleportation over non-maximally entangled pairs, analyzing different operational models and resource classes.

Contribution

It proposes a novel assisted teleportation framework with explicit feasibility regions and success probabilities, highlighting operational differences between resource classes.

Findings

Explicit feasibility regions for deterministic restoration with GHZ and W resources.

Operational inequivalence identified for W-class assistance.

Finite-shot optimal success probabilities for probabilistic restoration.

Abstract

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.