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Semidefinite programming relaxations for quantum correlations

Armin Tavakoli, Alejandro Pozas-Kerstjens , Peter Brown , and Mateus Araújo

Armin Tavakoli

Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden

Alejandro Pozas-Kerstjens

Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland and Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera 13–15, 28049 Madrid, Spain

Peter Brown

Télécom Paris—LTCI, Inria, Institut Polytechnique de Paris, 91120 Palaiseau, France

Mateus Araújo

Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid, Spain

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Rev. Mod. Phys. 96, 045006 – Published 4 December, 2024

DOI: https://doi.org/10.1103/RevModPhys.96.045006

Abstract

Semidefinite programs are convex optimization problems involving a linear objective function and a domain of positive-semidefinite matrices. Over the past two decades, they have become an indispensable tool in quantum information science. Many otherwise intractable fundamental and applied problems can be successfully approached by means of relaxation to a semidefinite program. This methodology is reviewed here in the context of quantum correlations. The manner in which the core idea of semidefinite relaxations can be adapted is discussed for a variety of research topics in quantum correlations, including nonlocality, quantum communication, quantum networks, entanglement, and quantum cryptography.

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Semidefinite programming relaxations for quantum correlations

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