Bounding the entanglement of a state from its spectrum
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.
Authors
- Anna Sanpera (ORCID: https://orcid.org/0000-0002-8970-6127)
- Guillem Müller-Rigat (ORCID: https://orcid.org/0000-0003-0589-7956)
- Jofre Abellanet-Vidal (ORCID: https://orcid.org/0009-0007-3118-0883)
- Albert Rico (ORCID: https://orcid.org/0000-0001-8211-499X)
Institutions
- Institució Catalana de Recerca i Estudis Avançats (ES)
- Universitat Autònoma de Barcelona (ES)
- Jagiellonian University (PL)
- University of Siegen (DE)
Publication Details
- Journal
- Quantum
- Published
- 2026-11-06
- DOI
- https://doi.org/10.22331/q-2026-11-06-2260
- Citations
- 4
- Primary Topic
- Quantum Information and Cryptography
- Type
- article
- Field-Weighted Citation Impact
- 5.26
Funders
- Ministerio de Ciencia, Innovación y Universidades
- European Commission
- Deutsche Forschungsgemeinschaft
- Generalitat de Catalunya
- Ministerio de Ciencia e Innovación
- Chinesisch-Deutsche Zentrum für Wissenschaftsförderung