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 . 060501/1-060501/6. ISSN 1079-7114

[img]
Preview
PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (358kB) | Preview

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 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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1103/PhysRevLett.117.060501
Related URLs:
URLURL Type
https://arxiv.org/abs/1604.02189v2UNSPECIFIED
Depositing User: Adesso, Gerardo
Date Deposited: 24 Feb 2017 09:44
Last Modified: 25 Feb 2017 00:48
URI: http://eprints.nottingham.ac.uk/id/eprint/40788

Actions (Archive Staff Only)

Edit View Edit View