### Abstract

Language | English |
---|---|

Article number | 060501 |

Number of pages | 6 |

Journal | Physical Review Letters |

Volume | 117 |

Issue number | 6 |

Early online date | 1 Aug 2016 |

DOIs | |

Publication status | Published - 5 Aug 2016 |

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### Keywords

- entanglement measure
- entanglement monogamy

### Cite this

*Physical Review Letters*,

*117*(6), [060501]. https://doi.org/10.1103/PhysRevLett.117.060501

}

*Physical Review Letters*, vol. 117, no. 6, 060501. https://doi.org/10.1103/PhysRevLett.117.060501

**Should entanglement measures be monogamous or faithful?** / Lancien, Cécilia; Di Martino, Sara; Huber, Marcus; Piani, Marco; Adesso, Gerardo; Winter, Andreas.

Research output: Contribution to journal › Letter

TY - JOUR

T1 - Should entanglement measures be monogamous or faithful?

AU - Lancien, Cécilia

AU - Di Martino, Sara

AU - Huber, Marcus

AU - Piani, Marco

AU - Adesso, Gerardo

AU - Winter, Andreas

PY - 2016/8/5

Y1 - 2016/8/5

N2 - "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.

AB - "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.

KW - entanglement measure

KW - entanglement monogamy

UR - http://journals.aps.org/prl/

U2 - 10.1103/PhysRevLett.117.060501

DO - 10.1103/PhysRevLett.117.060501

M3 - Letter

VL - 117

JO - Physical Review Letters

T2 - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 6

M1 - 060501

ER -