Simplest non-additive measures of quantum resources

Given an arbitrary state rho and some figure of merit E(rho), it is usually a hard problem to determine the value of E(rho(circle times N)). One noticeable exception is the case of additive measures, for which we simply have E(rho(circle times N)) = Ne, with e equivalent to E(rho). In this work, we study measures that can be described by E(rho(circle times N)) = E(e; N) not equal Ne, that is, measures for which the amount of resources of N copies is still determined by the single real variable e, but in a nonlinear way. If, in addition, the measures are analytic around e = 0, recurrence relations can be found for the Maclaurin coefficients of E for larger N. As an example, we show that the l(1)-norm of coherence is a non-trivial case of such a behavior.