and all of the decoherence dynamics in Eqs. 29a-29c will be governed by the changes in c 1,ξ and c 0,ξ . Ultimately, Eq. 39 only makes the choice that no arbitrary global phase is added to all coefficients since any other modification to the c j,ξ coefficients, besides adding a global phase, would incorrectly alter some of the reduced density matrix elements involving the {|j⟩} states.