Determination of the Schmidt number
Open accessAbstract
Optimized, necessary, and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure delivers equations similar to the eigenvalue problem of an operator. The properties of the solution of these equations will be studied. We solve these equations for classes of operators. The solutions will be applied to phase randomized two-mode squeezed-vacuum states in continuous variable systems.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
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 [46]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.1895 · Cited by 13,703 · see citing works
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Werner, R. F. (1989) · Physical Review A · doi:10.1103/physreva.40.4277 · Cited by 4,062 · see citing works
Entanglement measures and purification procedures
Vedral, V., & Plenio, M. B. (1998) · Physical Review A · doi:10.1103/physreva.57.1619 · Cited by 1,419 · see citing works
The Schmidt number as a universal entanglement measure
Sperling, J., & Vogel, W. (2011) · Physica Scripta · doi:10.1088/0031-8949/83/04/045002 · Cited by 96 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 1
- W. Vogel and D.-G. Welsch, Quantum Optics , 3rd ed. (Wiley-VCH, Warnheim, 2006).
Cited by
Sorted by citations
Experimental hierarchy of two-qubit quantum correlations without state tomography
Abo, S., Soubusta, J., Jiráková, K., Bartkiewicz, K., Černoch, A., Lemr, K., & Miranowicz, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-35015-9 · Cited by 17 · see citing works
“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 measure [43, 44] and can be determined experimentally via a witnessing approach [45].”
Background
- Authors
- Sperling, J., & Vogel, W.
- Affiliations
- University of Rostock (DE)
- ORCID
- Sperling, J.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2011-04-12
- Volume
- 83
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2082911488
- Cited by
- 47
- References
- 4
- Citations by year
- 2025: 1 · 2023: 2 · 2022: 1 · 2020: 2 · 2019: 1 · 2018: 1 · 2017: 4 · 2016: 2 · 2015: 4 · 2014: 10 · 2013: 8 · 2012: 7
- FWCI
- 8.55
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (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 optics and atomic interactions
- Keywords
- Schmidt number, quantum state identification, Hermitian operators, mixed quantum states, necessary and sufficient conditions, eigenvalue problem, continuous-variable quantum information, two-mode squeezed vacuum, phase randomization
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
