Additive entanglemement measures cannot be more than asymptotically continuous

Andrea Coladangelo; Debbie Leung

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Additive entanglemement measures cannot be more than asymptotically continuous

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arxiv 1910.11354 v1 pith:NLYNOAG5 submitted 2019-10-24 quant-ph hep-thmath-phmath.MP

Additive entanglemement measures cannot be more than asymptotically continuous

Andrea Coladangelo , Debbie Leung This is my paper

classification quant-ph hep-thmath-phmath.MP

keywords additiveasymptoticallycannotcontinuousentanglementinvariantproofunder

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In this short note, we show that any non-constant quantity defined on density matrices that is additive on tensor products and invariant under permutations cannot be "more than asymptotically continuous." The proof can be adapted to show that any additive entanglement measure (on any number of parties) that is invariant under local unitary operations also cannot be more than asymptotically continuous. The proof is a direct consequence of generalizing a protocol in arXiv:0804.4118 for embezzling entanglement.

Additive entanglemement measures cannot be more than asymptotically continuous

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