Entanglement monotones
Open accessAbstract
In the context of quantifying entanglement we study those functions of a multipartite state which do not increase under the set of local transformations. A mathematical characterization of these monotone magnitudes is presented. They are then related to optimal strategies of conversion of shared states. More detailed results are presented for pure states of bipartite systems. It is shown that more than one measure is required simultaneously in order to quantify completely the non-local resources contained in a bipartite pure state, while examining how this fact does not hold in the so-called asymptotic limit. Finally, monotonicity under local transformations is proposed as the only natural requirement for measures of entanglement.
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Whenever any given type of entanglement is to be generated from the resource state, it must already be present in the resource itself, as single-qubit operations cannot add entanglement.
“This implies that, whenever any given type of entanglement-as quantified by an appropriate entanglement measure 81 -is to be generated from the resource state, it must already be present in the resource itself, as single-qubit operations cannot add entanglement to the system.”
From Measurement-based quantum computation (2009) · cites this paper as [81]
Any quantity that is supposed to quantify entanglement needs to be monotonously decreasing under operations that can create or increase only classical correlations.
“Any quantity that is supposed to quantify entanglement needs to be monotonously decreasing under such operations [25,41].”
From Measures and dynamics of entangled states (2005) · cites this paper as [25]
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- Authors
- Vidal, G.
- Affiliations
- Universitat de Barcelona (ES)
- Corresponding author
- Vidal, Guifré
- ORCID
- Vidal, Guifré
- Venue
- Journal of Modern Optics
- Publisher
- Informa UK Limited
- Published
- 2000-02
- Volume
- 47
- Issue
- 2-3
- Pages
- 355-376
- ISSN
- 0950-0340 (ISSN-L)
- 1362-3044
- OpenAlex
- W2281702696
- Semantic Scholar
- 08690e9d3245f0aac7712f299c317585e28337df
- Cited by
- 821
- References
- 13
- Citations by year
- 2026: 23 · 2025: 56 · 2024: 44 · 2023: 40 · 2022: 42 · 2021: 34 · 2020: 37 · 2019: 37 · 2018: 28 · 2017: 25 · 2016: 37 · 2015: 33 · 2014: 27 · 2013: 22 · 2012: 29
- FWCI
- 37.08
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Modern Optics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- entanglement monotones, entanglement measures, local transformations, multipartite entanglement, bipartite pure states, entanglement conversion
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