The Schmidt number as a universal entanglement measure
Open accessAbstract
The class of local invertible operations is defined and the invariance of entanglement under such operations is established.For the quantification of entanglement, universal entanglement measures are defined, which are invariant under local invertible transformations.They quantify entanglement in a very general sense.It is shown that the Schmidt number is a universal entanglement measure, which is most important for the general amount of entanglement.For special applications, pseudo-measures are defined to quantify the useful entanglement for a certain quantum task.The entanglement quantification is further specified by operational measures, which include the accessible observables by a given experimental setup.
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The first non-classicality criterion (Bromberg et al.) states that when two incoherent classical beams are coupled to two distinct input waveguides, the resulting intensity correlations always satisfy Γ_ns,ni > (2/3)√(Γ_ns,ns Γ_ni,ni).
“The first one, established by Bromberg et al. [32, 40], states that when two incoherent classical beams are coupled to two distinct input waveguides, the resulting intensity correlations Γ n s ,n i = | Ψ( n s , n i ) | 2 always satisfy the following”
From Tailoring quantum walks in integrated photonic lattices (2025) · cites this paper as [32]
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Self-citation
- Authors
- Sperling, J., & Vogel, W.
- Affiliations
- University of Rostock (DE)
- ORCID
- Sperling, J
- Venue
- Physica Scripta
- Publisher
- IOP Publishing
- Published
- 2011-03-08
- Volume
- 83
- Issue
- 4
- Pages
- 045002
- ISSN
- 0031-8949 (ISSN-L)
- 1402-4896
- OpenAlex
- W2094087432
- Cited by
- 96
- References
- 37
- Citations by year
- 2026: 3 · 2025: 10 · 2024: 4 · 2023: 4 · 2022: 6 · 2021: 8 · 2020: 8 · 2019: 8 · 2018: 1 · 2017: 6 · 2016: 3 · 2015: 7 · 2014: 11 · 2013: 8 · 2012: 7
- FWCI
- 8.25
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physica Scripta (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft (SFB 652)
- 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, entanglement measures, entanglement quantification, quantum entanglement
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