  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.
