Should entanglement measures be monogamous or faithful?

Lancien, C�cilia; Di Martino, Sara; Huber, Marcus; Piani, Marco; Adesso, Gerardo; Winter, Andreas

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.

Citation

Lancien, C., Di Martino, S., Huber, M., Piani, M., Adesso, G., & Winter, A. (2016). Should entanglement measures be monogamous or faithful?. Physical Review Letters, 117, Article 060501. https://doi.org/10.1103/PhysRevLett.117.060501

• Journal Article Type: Article
• Acceptance Date: Jul 12, 2016
• Publication Date: Aug 1, 2016
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Feb 24, 2017
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 117
• Article Number: 060501
• DOI: https://doi.org/10.1103/PhysRevLett.117.060501
• Public URL: https://nottingham-repository.worktribe.com/output/797742
• Publisher URL: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.060501
• Related Public URLs: https://arxiv.org/abs/1604.02189v2