Strong superadditivity of the entanglement of formation follows from its additivity

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Abstract
The additivity of both the entanglement of formation and the classical channel capacity is known to be a consequence of the strong superadditivity conjecture. We show that, conversely, the strong superadditivity conjecture follows from the additivity of the entanglement of formation; this means that the two conjectures are equivalent and that the additivity of the classical channel capacity is a consequence of them.

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