### Abstract

In quantum information processing, non-additivity refers to the fact that the performance of some task can be improved by the global use of separate resources. In the extreme case known as superactivation, the global use of resources may render possible an otherwise impossible task. Non-additivity and superactivation are features with a purely quantum origin. The entanglement of purification is a measure of total correlations for bipartite quantum states: correlations are quantified in terms of the entanglement as measured by the entropy of entanglement that two parties would need to share to create their shared state by local operations. The average entanglement of purification per shared copy of a given quantum state, in the limit of many copies i.e., its so-called regularization quantifies the minimum entanglement cost of a bipartite state when only local operations and negligible classical communications are allowed. Recently, numerical evidence was provided for the non-additivity of the entanglement of purification. If this result was confirmed, it would mean that the entanglement of purification and its regularization differ, implying another quantum advantage in collective encoding in information theory, namely, in quantum dense coding. The quantum correlation complexity is a variation of the entanglement of purification, with the entanglement cost of a single copy of a bipartite quantum state quantified in terms of local rank. We show that the quantum correlation complexity recovers the regularization of the entanglement of purification in the standard framework of information theory, in particular allowing for asymptotically vanishing errors. Also, we explicitly construct an example showing the non-additivity of the quantum correlation complexity, which we interpret as supporting evidence of the non-additivity of the entanglement of purification. Moreover we prove that its classical corresponding quantity, the randomized correlation complexity, is additive.