Mixed-state entanglement and distillation: Is there a ‘bound’ entanglement in nature?
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It is shown that if a mixed state can be distilled to the singlet form it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two qualitatively different types of entanglement: ``free'' entanglement which is distillable, and ``bound'' entanglement which cannot be brought to the singlet form useful for quantum communication purposes. A possible physical meaning of the result is discussed.
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For two three-dimensional systems, or more complicated ones, one can find states which are entangled but from which no maximally entangled state can be distilled (bound entangled).
“An interesting feature of the theory of entanglement of mixed states is that for two three dimensional systems, or for more complicated ones, one can find states which are entangled, but from which no maximally entangled state can be distilled 10 (Horodecki, Horodecki and Horodecki, 1998).Such states are called bound entangled.”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Horodecki, Horodecki and Horodecki, 1998
In higher dimensions there exist entangled states that are not detected by the ppt criterion.
“However, in higher dimensions there exist entangled states [39,40] that are not detected by the ppt criterion.”
From Measures and dynamics of entangled states (2005) · cites this paper as [39]
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- Authors
- Horodecki, M., Horodecki, P., & Horodecki, R.
- Affiliations
- University of Gdańsk (PL)
- Gdańsk University of Technology (PL)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1998-06-15
- Volume
- 80
- Issue
- 24
- Pages
- 5239-5242
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2003989474
- Cited by
- 1,208
- References
- 25
- Citations by year
- 2026: 32 · 2025: 57 · 2024: 56 · 2023: 37 · 2022: 46 · 2021: 46 · 2020: 43 · 2019: 47 · 2018: 40 · 2017: 36 · 2016: 35 · 2015: 34 · 2014: 43 · 2013: 56 · 2012: 56
- FWCI
- 39.01
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (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
- bound entanglement, entanglement distillation, mixed-state entanglement, singlet state, quantum communication
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