  For the tensor of coherences parametrization of a multiqubit density
operator, we provide an explicit formulation of the corresponding unitary
dynamics at infinitesimal level. The main advantage of this formalism (clearly
reminiscent of the idea of ``coherences'' and ``coupling Hamiltonians'' of spin
systems) is that the pattern of correlation between qubits and the pattern of
infinitesimal correlation are highlighted simultaneously and can be used
constructively for qubit manipulation. For example, it allows to compute
explicitly a Rodrigues' formula for the one-parameter orbits of nonlocal
Hamiltonians. The result is easily generalizable to orbits of Cartan
subalgebras and allows to write the Cartan decomposition of unitary propagators
as a linear action.
