Should entanglement measures be monogamous or faithful?

Lancien, Cécilia and Di Martino, Sara and Huber, Marcus and Piani, Marco and Adesso, Gerardo and Winter, Andreas (2016) Should entanglement measures be monogamous or faithful? Physical Review Letters, 117 (6). 060501. ISSN 1079-7114 (https://doi.org/10.1103/PhysRevLett.117.060501)

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Abstract

"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 affirmativein 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.

ORCID iDs

Lancien, Cécilia, Di Martino, Sara, Huber, Marcus, Piani, Marco ORCID logoORCID: https://orcid.org/0000-0002-4698-9497, Adesso, Gerardo and Winter, Andreas;
  • Item type:Article
    ID code:57126
    Dates:
    Date
    Event
    5 August 2016
    Published
    1 August 2016
    Published Online
    12 July 2016
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:27 Jul 2016 08:43
    Last modified:11 Nov 2024 11:26
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/57126
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