Representing multiqubit unitary evolutions via Stokes tensors

For the Stokes tensor parametrization of a multiqubit density operator, an explicit formulation of the corresponding unitary dynamics at the infitesimal level was developed. The main advantage of this formalism 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. The idea of associating coherences to the degrees of freedom of qubits through the corresponding Hamiltonians is common in spin systems in magnetic fields. The result obtained is easily generalizable to orbits of Cartan subalgebras and allows the expression of Cartan decomposition of unitary propagators as a linear action.}