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Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)

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.

preprint2012arXivOpen access
Jianxin ChenAndreas Winter
math.ITInformation Theoryquant-ph
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Jianxin ChenAndreas Winter

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