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We study the entanglement cost under quantum operations preserving thepositivity of the partial transpose (PPT-operations). We demonstrate that thiscost is directly related to the logarithmic negativity, thereby providing theoperational interpretation for this easily computable entanglement measure. Asexamples we discuss general Werner states and arbitrary bi-partite Gaussianstates. Equipped with this result we then prove that for the anti-symmetricWerner state PPT-cost and PPT-entanglement of distillation coincide giving thefirst example of a truly mixed state for which entanglement manipulation isasymptotically reversible.Comment: 4 pages, 1 figur

Entanglement Cost under Positive-Partial-Transpose-Preserving Operations