Geometry of Two-Qubit State and Intertwining Quaternionic Conformal Mapping Under Local Unitary Transformations

In this paper the geometry of two-qubit systems under local unitary group $SO(2)\otimes SU(2)$ is discussed. It is shown that the quaternionic conformal map intertwines between this local unitary subgroup of $Sp(2)$ and the quaternionic M\"{o}bius transformation which is rather a generalization of the results of Lee et al (2002 Quantum Inf. Process. 1 129).