Recently, W. Slofstra proved that the set of quantum correlations is not closed. We prove that the set of synchronous quantum correlations is not closed, which implies his result, by giving an example of a synchronous game that has a perfect quantum approximate strategy but no perfect quantum strategy. We also exhibit a graph for which the quantum independence number and the quantum approximate independence number are different. We prove new characterisations of synchronous quantum approximate correlations and synchronous quantum spatial correlations. We solve the synchronous approximation problem of Dykema and the second author, which yields a new equivalence of Connes' embedding problem in terms of synchronous correlations.
Lifting the maximally-entangledness assumption in robust self-testing for synchronous games
Delft Institute of Applied Mathematics, TU Delft（代尔夫特理工大学应用数学研究所）；QMATH, Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系QMATH）
The hypergraph isomorphism game, Hopf algebras and Galois extensions
Research Institute of Mathematics Seoul National University（首尔大学数学研究所）；NextQuantum Innovation Research Center, Department of Physics and Astronomy Seoul National University（首尔大学物理与天文学系下一代量子创新中心）；School of Electrical and Computer Engineering National Technical University of Athens（雅典国立技术大学电气与计算机工程学院）；Institute of Mathematics of the Polish Academy of Sciences（波兰科学院数学研究所）；Department of Mathematics Dartmouth College（达特茅斯学院数学系）
