Abstract
In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman---Murakami---Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, which is generated by both the Temperley---Lieb projector and the Yang---Baxter gate. We describe quantum teleportation using the Temperley---Lieb projector and the Yang---Baxter gate, respectively, and study teleportation-based quantum computation using the Yang---Baxter gate. On the other hand, we exploit the extended Temperley---Lieb diagrammatical approach to clearly show that the tangle relations of the BMW algebra have a natural interpretation of quantum teleportation. Inspired by this interpretation, we construct a general representation of the tangle relations of the BMW algebra and obtain interesting representations of the BMW algebra. Therefore, our research sheds a light on a link between quantum information science and low-dimensional topology.
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