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Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt) (1206.1307v1)
Published 6 Jun 2012 in quant-ph, cs.IT, and math.IT
Abstract: 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.