Quantum teleportation and Birman-Murakami-Wenzl algebra

TL;DR

This paper explores the connection between quantum teleportation and the Birman-Murakami-Wenzl algebra, demonstrating how algebraic structures underpin quantum information processes and providing new representations linking topology and quantum computation.

Contribution

It introduces a novel interpretation of BMW algebra tangle relations in quantum teleportation and constructs new algebraic representations relevant to quantum information science.

Findings

Quantum teleportation can be described using BMW algebra generators.

The extended Temperley-Lieb diagrammatic approach clarifies the topological interpretation.

New representations of BMW algebra are constructed with potential applications in quantum computation.

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.