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 ${\check{R}}_{i,i+1}(\theta ,\varphi )$-matrix, where $\varphi =\omega t$ is time-dependent while $\theta$ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.

6 pages, 2 figures. Published version

References in corpus (3)

• High-speed linear optics quantum computing using active feed-forward
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Measurement of geometric phase for mixed states using single photon interferometry

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• Geometric representations of braid and Yang-Baxter gates
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