 Magic basis

A Bell basis with phases chosen so that local special-unitary transformations of the two qubits are represented by real four-dimensional rotations. For one standard ordering it is ${\Phi }_{+},i{\Phi }_{-},i{\Psi }_{+},{\Psi }_{-}$. Permuting these vectors changes generator conventions but preserves the invariant concurrence $|{\sum }_j{b}_j^2|$.^[ref]