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arXiv · 2605.22226

Geometric Construction of Optimal Teleportation Witnesses

Yanning Jia·Fenzhuo Guo·Mengxuan Bai·Mengyan Li·Haifeng Dong·Fei Gao
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Abstract

Not all entangled states are useful for quantum teleportation. We present a geometric method to construct optimal teleportation witnesses, which provide operational necessary and sufficient criteria for identifying the teleportation usefulness of arbitrary two-qudit entangled states. Specifically, by developing a two-layer iterative cutting-plane algorithm to solve the shortest distance problem from the target state $\rho$ to the convex set $S$ of useless states, we obtain the projection point $\sigma^* \in S$ and then construct the optimal teleportation witness from the projection geometry. Moreover, the shortest distance $D(\rho)$ obtained during this construction also serves as a necessary and sufficient criterion for usefulness. We apply our method to identify the teleportation usefulness of three classes of entangled states.

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Yanning Jia, Fenzhuo Guo, Mengxuan Bai, Mengyan Li, Haifeng Dong, Fei Gao. 2026-05-21. Geometric Construction of Optimal Teleportation Witnesses. https://arxiv.org/abs/2605.22226

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