Quantum Entanglement Math Background Notes

Each of these examples turns out to be a surface in R 2 or C 2 = R 2 . The trivial group is a single point and the general linear group is an open subset of R 2 or C 2 . The unitary group U(1) is the unit circle S in C = R, and the special orthogonal group SO(2) turns out to be the same thing even though it lives in R. The special unitary group SU(2) is the three dimensional sphere S (even though it lives in C = R). Of particular interest in quantum information is the group SU(2) of 2×2 unitary matrices with determinant 1.