Should Entanglement Measures be Monogamous or Faithful?

Cécilia Lancien, Sara Di Martino, Marcus Huber, Marco Piani, Gerardo Adesso, Andreas Winter

Research output: Contribution to journalArticleResearchpeer-review

37 Citations (Scopus)

Abstract

© 2016 American Physical Society. "Is entanglement monogamous?" asks the title of a popular article [B. Terhal, IBM J. Res. Dev. 48, 71 (2004)], celebrating C. H. Bennett's legacy on quantum information theory. While the answer is affirmative in the qualitative sense, the situation is less clear if monogamy is intended as a quantitative limitation on the distribution of bipartite entanglement in a multipartite system, given some particular measure of entanglement. Here, we formalize what it takes for a bipartite measure of entanglement to obey a general quantitative monogamy relation on all quantum states. We then prove that an important class of entanglement measures fail to be monogamous in this general sense of the term, with monogamy violations becoming generic with increasing dimension. In particular, we show that every additive and suitably normalized entanglement measure cannot satisfy any nontrivial general monogamy relation while at the same time faithfully capturing the geometric entanglement structure of the fully antisymmetric state in arbitrary dimension. Nevertheless, monogamy of such entanglement measures can be recovered if one allows for dimension-dependent relations, as we show explicitly with relevant examples.
Original languageEnglish
Article number060501
JournalPhysical Review Letters
Volume117
Issue number6
DOIs
Publication statusPublished - 1 Aug 2016

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