# Braiding transformation, entanglement swapping and Berry phase in entanglement space

## TL;DR

This paper explores how braiding transformations can describe quantum entanglement, enabling entanglement swapping, GHZ and cluster state generation, and analysis of Berry phases in entanglement space using a Hamiltonian derived from unitary braiding operators.

## Contribution

It introduces a braiding-based framework for entanglement manipulation and connects it with Berry phase analysis, providing a novel approach to quantum state control.

## Key findings

- Braiding operators realize entanglement swapping.
- GHZ and cluster states are generated via braiding transformations.
- Berry phase in entanglement space is investigated using a derived Hamiltonian.

## Abstract

We show that braiding transformation is a natural approach to describe quantum entanglement, by using the unitary braiding operators to realize entanglement swapping and generate the GHZ states as well as the linear cluster states. A Hamiltonian is constructed from the unitary $\check{R}_{i,i+1}(\theta,\phi)$-matrix, where $\phi=\omega t$ is time-dependent while $\theta$ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.