Berry phase and entanglement of 3 qubits in a new Yang-Baxter system

Details Berry phase and entanglement of 3 qubits in a new Yang-Baxter system Berry phase and entanglement of 3 qubits in a new Yang-Baxter system

2009-04-23

arxiv.org/abs/0904.3621v1

J. Math. Phys. 50, 083509 (2009)

Physics

Quantum Physics

Scientific paper

10.1063/1.3177295

In this paper we construct a new $8\times8$ $\mathbb{M}$ matrix from the $4\times4$ $M$ matrix, where $\mathbb{M}$ / $M$ is the image of the braid group representation. The $ 8\times8 $ $\mathbb{M}$ matrix and the $4\times4$ $M$ matrix both satisfy extraspecial 2-groups algebra relations. By Yang-Baxteration approach, we derive a unitary $ \breve{R}(\theta, \phi)$ matrix from the $\mathbb{M}$ matrix with parameters $\phi$ and $\theta$. Three-qubit entangled states can be generated by using the $\breve{R}(\theta,\phi)$ matrix. A Hamiltonian for 3 qubits is constructed from the unitary $\breve{R}(\theta,\phi)$ matrix. We then study the entanglement and Berry phase of the Yang-Baxter system.

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