# Local Unitary Representation of Braids and N-Qubit Entanglements

## TL;DR

This paper explores how local unitary representations of braid groups relate to entanglement properties in N-qubit systems, linking topological braiding operations to quantum entanglement through stabilizer codes.

## Contribution

It establishes a connection between braid group representations and entanglement in N-qubit states, providing new insights into topological and quantum entanglement.

## Key findings

- Separable states correspond to specific braid diagrams
- Braid operations influence entanglement structure
- Topological features relate to quantum entanglement

## Abstract

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 $|\Psi\rangle$, where the N-qubit state $|\Psi\rangle$ is obtained by applying the braiding operation on the natural basis. Specifically, we show that the separability of $|\Psi\rangle=\mathcal{B}|0\rangle^{\otimes N}$ 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.