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

Jianxin Chen; Andreas Winter

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arXiv · 1206.1307

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

Jianxin Chen·Andreas Winter

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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.

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Jianxin Chen, Andreas Winter. 2012-06-06. Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt). https://arxiv.org/abs/1206.1307

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