Semidefinite programming relaxations for quantum correlations
Sometimes a mathematical tool emerges as uniquely useful and even a defining feature within some branch of physics such as Feynman diagrams. In quantum information theory, the semidefinite program (SDP) has emerged as such a tool. SDP is an optimization task in which a linear objective function is maximized over a set of Hermitian matrices with positive eigenvalues. This review discusses the highly efficient algorithms available for the SDP, and shows how comprehensively the SDP has been deployed in problems of entanglement characterization, quantum nonlocality, quantum channel capacities, and the bounding of ground-state energies.
Authors
- Armin Tavakoli (ORCID: https://orcid.org/0000-0001-9136-7411)
- Alejandro Pozas-Kerstjens (ORCID: https://orcid.org/0000-0002-3853-3545)
- Peter Brown (ORCID: https://orcid.org/0000-0001-9593-0136)
- Mateus Araújo (ORCID: https://orcid.org/0000-0003-0155-354X)
Institutions
- Universidad de Valladolid (ES)
- University of Geneva (CH)
- Lund University (SE)
- Institute of Mathematical Sciences (ES)
Publication Details
- Journal
- Reviews of Modern Physics
- Published
- 2024-12-04
- DOI
- https://doi.org/10.1103/revmodphys.96.045006
- Citations
- 43
- Primary Topic
- Quantum Information and Cryptography
- Type
- article
- Field-Weighted Citation Impact
- 14.59
Funders
- Wenner-Gren Foundation
- Comunidad de Madrid
- National Centres of Competence in Research SwissMAP
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Austrian Science Fund
- Universidad Complutense de Madrid
- Knut och Alice Wallenbergs Stiftelse
- Ministerio de Ciencia e Innovación
- Horizon 2020 Framework Programme
- Consejo Superior de Investigaciones Científicas