Speaker: 许湘灵，Inria Paris-Saclay

Inviter: 王杰副研究员

Title: A Generalized NPA Moment-SOS Hierarchy and Its Application to Quantum Information Theory

Language: Chinese

Time & Venue: 2025.12.26 14:00-16:00 南楼N514

Abstract: The NPA hierarchy is a powerful application of moment-sum-of-squares (SOS) optimization techniques to the study of multipartite nonlocal games, which are central in the quantum information theory. Recent work [Baroni et al. 2025] has established an equivalence between the multipartite nonlocal games and a more general class of sequential games. This generalization requires the inclusion of completely positive maps in the problem formulation, which goes beyond the standard NPA framework. In this talk, we introduce a generalized moment-SOS hierarchy that directly encodes these completely positive maps and their associated constraints. We show that this hierarchy is equivalent to the standard NPA hierarchy in the limit. As a key application, we prove that any “almost feasible” solution is necessarily close to a true solution of our hierarchy. This result resolves a key open problem concerning the quantum soundness of compiled nonlocal games, a highly active research area in quantum information and cryptography.