Local Unitary Representation of Braids and N-Qubit Entanglements

In this paper, by utilizing the idea of stabilizer codes, we give some relationships between one local unitary representation of braid group in N-qubit tensor space and the corresponding entanglement properties of the N-qubit pure state $|Psirangle$, where the N-qubit state $|Psirangle$ is obtained by applying the braiding operation on the natural basis. Specifically, we show that the separability of $|Psirangle=mathcal{B}|0rangle^{otimes N}$ is closely related to the diagrammatic version of the braid operator $mathcal{B}$. This may provide us more insights about the topological entanglement and quantum entanglement.