%0 Journal Article %D 2012 %T Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt) %A Jianxin Chen %A Andreas Winter %X We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification is not additive. %8 2012/06/06 %G eng %U http://arxiv.org/abs/1206.1307v1