TY - JOUR T1 - Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt) Y1 - 2012 A1 - Jianxin Chen A1 - Andreas Winter AB - 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. UR - http://arxiv.org/abs/1206.1307v1 ER -