Should entanglement measures be monogamous or faithful?
“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 quantita...
| Main Authors: | , , , , , |
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| Format: | Article |
| Published: |
American Physical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40788/ |
| _version_ | 1848796133580603392 |
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| author | Lancien, Cécilia Di Martino, Sara Huber, Marcus Piani, Marco Adesso, Gerardo Winter, Andreas |
| author_facet | Lancien, Cécilia Di Martino, Sara Huber, Marcus Piani, Marco Adesso, Gerardo Winter, Andreas |
| author_sort | Lancien, Cécilia |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | “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. |
| first_indexed | 2025-11-14T19:43:08Z |
| format | Article |
| id | nottingham-40788 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:08Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-407882020-05-04T17:58:31Z https://eprints.nottingham.ac.uk/40788/ Should entanglement measures be monogamous or faithful? Lancien, Cécilia Di Martino, Sara Huber, Marcus Piani, Marco Adesso, Gerardo Winter, Andreas “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. American Physical Society 2016-08-01 Article PeerReviewed Lancien, Cécilia, Di Martino, Sara, Huber, Marcus, Piani, Marco, Adesso, Gerardo and Winter, Andreas (2016) Should entanglement measures be monogamous or faithful? Physical Review Letters, 117 . 060501/1-060501/6. ISSN 1079-7114 http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.060501 doi:10.1103/PhysRevLett.117.060501 doi:10.1103/PhysRevLett.117.060501 |
| spellingShingle | Lancien, Cécilia Di Martino, Sara Huber, Marcus Piani, Marco Adesso, Gerardo Winter, Andreas Should entanglement measures be monogamous or faithful? |
| title | Should entanglement measures be monogamous or faithful? |
| title_full | Should entanglement measures be monogamous or faithful? |
| title_fullStr | Should entanglement measures be monogamous or faithful? |
| title_full_unstemmed | Should entanglement measures be monogamous or faithful? |
| title_short | Should entanglement measures be monogamous or faithful? |
| title_sort | should entanglement measures be monogamous or faithful? |
| url | https://eprints.nottingham.ac.uk/40788/ https://eprints.nottingham.ac.uk/40788/ https://eprints.nottingham.ac.uk/40788/ |