Braiding transformation, entanglement swapping and Berry phase in entanglement space

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.