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arXiv:2602.11218

Algebraic and Topological Study of Bell States and Quantum Teleportation

Yong Zhang, Wei Zeng, Ming Lian

quant-phSubmitted Feb 11, 2026• Announced Feb 12, 2026• 0 citations• Revised Sep 4, 2026 (v2)
v1 · Feb 11, 2026v2 · Sep 4, 2026
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Abstract

Bell states and quantum teleportation play crucial roles in quantum information and computation. However, a comprehensive theoretical study of both topics remains to be carried out. This work aims to investigate key algebraic properties of generalized Bell states and explore the topological features of quantum teleportation. First, the basis theorem and the basis group are introduced to show that the extension of a generalized Bell basis by a unitary matrix still forms an orthonormal basis. Then, a twist operator is defined to establish a connection between a generalized multi-qubit Bell state and a tensor product of two-qubit Bell states. In addition, the Temperley--Lieb algebra, the braid group relations, and the Yang--Baxter equation are employed to provide a topological description of generalized Bell states and quantum teleportation. The results demonstrate that our approach not only offers a clear illustration of relevant quantum information protocols but also reveals the topological nature of quantum entanglement and teleportation.

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36 pages, 21 figures

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