Geometric Construction of Optimal Teleportation Witnesses

@misc{jia2026geometric,
  title = {{Geometric Construction of Optimal Teleportation Witnesses}},
  author = {Yanning Jia and Fenzhuo Guo and Mengxuan Bai and Mengyan Li and Haifeng Dong and Fei Gao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.22226},
  eprint = {2605.22226},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.22226},
}

TY  - UNPB
TI  - Geometric Construction of Optimal Teleportation Witnesses
AU  - Yanning Jia
AU  - Fenzhuo Guo
AU  - Mengxuan Bai
AU  - Mengyan Li
AU  - Haifeng Dong
AU  - Fei Gao
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2605.22226
UR  - https://arxiv.org/abs/2605.22226
AB  - 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 ρ to the convex set S of useless states, we obtain the projection point σ^* ∈ S and then construct the optimal teleportation witness from the projection geometry. Moreover, the shortest distance D(ρ) 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.
ER  -