world. Moreover, in quantum computing, a new important development is the probabilistic implementation of a nonlocal gate by using a single non-maximally entangled state[27]. The success fidelity maintains a high level though the state shared is partially entangled. 

We believe that our work provide a connection among particle physics, quantum informa- tion and quantum algebra, and the result may shed new light on entanglement controlling in quantum computing. 

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