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Characterization of entanglement transformation via group representation theory

Li-Xiang Cen·Xin-Qi Li·YiJing Yan
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Abstract

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo orthonormalized. The two-to-one homomorphism is then established for the group $SL(2,C)\otimes SL(2,C)$ onto the $SO(4,C)$. It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.

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Li-Xiang Cen, Xin-Qi Li, YiJing Yan. 2002-12-30. Characterization of entanglement transformation via group representation theory. https://doi.org/10.1088/0305-4470/36/49/009

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