Schmidt-number witnesses and bound entanglement
Open accessAbstract
The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by studying Schmidt-number witnesses that detect it. We present a canonical form of such witnesses and provide constructive methods for their optimization. Finally, we present strong evidence that all bound entangled states with positive partial transpose in ${\mathcal{C}}^{3}\ensuremath{\bigotimes}{\mathcal{C}}^{3}$ have Schmidt number 2.
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Another experimental approach to determine entanglement without QST can be based on measuring a bipartite Schmidt number, which satisfies conditions of a good entanglement measure and can be determined experimentally via a witnessing approach.
“Another experimental approach to determine entanglement of a given state without QST can be based on measuring a bipartite Schmidt number, which satisfies various conditions of a good entanglement measure44,45 and can be determined experimentally via a witnessing approach46.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [45]
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References 26 · Cited by 233
Research works printed but not linked: 4
- [1]D. Bouwmeester, A. Ekert, and A. Zeilinger (Eds.), 'The Physics of Quantum Information', (Springer, Heidelberg, 2000).
- [3]M. Horodecki, P. Horodecki and R. Horodecki, in 'Quantum Information -Basic Concepts and Experiments' , Eds. G. Alber and M. Weiner, in print (Springer, Berlin, 2000).
- [17](a) M. Lewenstein et al. , quant-ph/0005112; (b) M. Lewenstein et al. , quant-ph/0005014, Phys. Rev. A XXX (2000). · arXiv
- [22](a) C. H. Bennett et al. , Phys. Rev. Lett. 82 , 5385 (1999); (b) D. Bruß and A. Peres, Phys. Rev. A 61 , 30301(R) (2000); (c) P. Horodecki and M. Lewenstein, quant-ph/0001035, Phys. Rev. Lett 85 , 2657 (2000). · arXiv
- Authors
- Sanpera, A., Bruß, D., & Lewenstein, M.
- Affiliations
- Leibniz University Hannover (DE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2001-04-09
- Volume
- 63
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1982683415
- Cited by
- 233
- References
- 26
- Citations by year
- 2026: 14 · 2025: 20 · 2024: 12 · 2023: 9 · 2022: 9 · 2021: 8 · 2020: 4 · 2019: 9 · 2018: 10 · 2017: 6 · 2016: 10 · 2015: 8 · 2014: 14 · 2013: 12 · 2012: 15
- FWCI
- 3.72
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (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
- Schmidt number, bound entanglement, mixed states, positive partial transpose, Schmidt rank
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