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Should entanglement measures be monogamous or faithful?

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


Cécilia Lancien

Sara Di Martino

Marcus Huber

Marco Piani

Andreas Winter


“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.


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,

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
Public URL
Publisher URL
Related Public URLs
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf


1604.02189.pdf (359 Kb)

Copyright Statement
Copyright information regarding this work can be found at the following address:

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