Semidefinite programming relaxations for quantum correlations

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.