Geometric structure of quantum correlators via semidefinite programming

Abstract

Quantum information leverages correlations between spacelike separated parties in order to perform useful tasks such as secure communication and randomness certification. Nevertheless, not much is known about the intricate geometric features of the set quantum correlators. In this paper we study the structure of the set of quantum correlators using semidefinite programming, more precisely the boundary, extreme, and exposed points. We obtain quantum Bell inequalities characterizing a certain class of bipartite scenarios. In the case of two dichotomic measurements, extremal quantum correlators coincide with the correlators that uniquely determine the state and measurement operators, a property known as self-testing. We illustrate the usefulness of our theoretical findings with many examples and extensive computational work.

Locations

• Physical review. A/Physical review, A - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View