Total correlations as multi-additive entanglement monotones

We propose general conditions for a measure of total correlations as an entanglement monotone using its pure and mixed convex-roof extension. In doing so, we derive crucial theorems and propose a concrete candidate for a total correlation measure which is a multi-additive multipartite entanglement monotone. We perform numerical simulations that show, comparatively, the dependence of the proposed coherent total correlation measure on the size of the register for several different quantum states and for global and pairwise correlation measures. We also show how to simplify some of the conditions required for monotonicity, in particular that a function must be non-increasing under local operations and classical communications.