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Peer-reviewedCC BY 4.0Quantum

Bounding the entanglement of a state from its spectrum

  • Jofre Abellanet-Vidal1
  • Guillem Müller-Rigat2
  • Albert Rico1,3
  • Anna Sanpera1,4
4 affiliations
  1. 1Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain.
  2. 2Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland.
  3. 3Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany.
  4. 4ICREA – Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain.
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Abstract

We introduce a framework to upper bound the entanglement content of a bipartite quantum state from its spectrum alone. Using linear maps and their inverses, we derive rigorous constraints on the maximal entanglement that can be activated under global unitary transformations. We use as entanglement quantifiers the negativity and the Schmidt number; however, our framework is general and applies to any other entanglement measure. Our approach yields compact analytical sufficient criteria for bounding the entanglement of full-rank states in arbitrary dimensions and reveals new spectral constraints on Schmidt number witnesses.

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Cite

BibTeXRIS
BibTeX
@article{abellanetvidal2026bounding,
  title = {{Bounding the entanglement of a state from its spectrum}},
  author = {Jofre Abellanet-Vidal and Guillem Müller-Rigat and Albert Rico and Anna Sanpera},
  journal = {Quantum},
  year = {2026},
  month = nov,
  doi = {10.22331/q-2026-11-06-2260},
  url = {https://quantum-journal.org/papers/q-2026-11-06-2260/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Bounding the entanglement of a state from its spectrum
AU  - Jofre Abellanet-Vidal
AU  - Guillem Müller-Rigat
AU  - Albert Rico
AU  - Anna Sanpera
PY  - 2026
DA  - 2026/11/06
JO  - Quantum
DO  - 10.22331/q-2026-11-06-2260
UR  - https://quantum-journal.org/papers/q-2026-11-06-2260/
AB  - We introduce a framework to upper bound the entanglement content of a bipartite quantum state from its spectrum alone. Using linear maps and their inverses, we derive rigorous constraints on the maximal entanglement that can be activated under global unitary transformations. We use as entanglement quantifiers the negativity and the Schmidt number; however, our framework is general and applies to any other entanglement measure. Our approach yields compact analytical sufficient criteria for bounding the entanglement of full-rank states in arbitrary dimensions and reveals new spectral constraints on Schmidt number witnesses.
SN  - 2521-327X
ER  -