De Vern Paulsen
In recent years a deep connection has been found between Connnes’ embedding problem and Tsirelson’s questions about various sets of probabilistic quantum correlations, called local, quantum, quantum approximate, and quantum commuting correlations, respectively. The most fruitful approach to studying these questions and separating these types of correlations has been through the theory of perfect strategies for finite input-output games. Synchronous games are a special family of these games. Affiliated with each synchronous game is a C_-algebra such that the game has a perfect strategy of each of these four types if and only if the C_-algebra has, respectively, a trace of one of four types. Using this theory and the work of Slofstra, we are able to construct two graphs such that their “graph isomorphism game” has a perfect quantum approximate strategy but no perfect quantum strategy. This, in turn, implies that the set of synchronous quantum correlations is not closed.
De Li Gao
De Rolf Gohm
De Aurelian Gheondea
De Ignacio Villanueva
De Michael Brannan
De Douglas Farenick
De David Pérez-García
De Yoshiko Ogata
De Runyao Duan
De Edward Effros
De Hiroyuki Osaka
De Fumio Hiai
De Magdalena Musat
De Nicholas LaRacuente
De Dan Voiculescu
De Aram Harrow
De Seung-Hyeok Kye
De Albert Schwarz
De Amine Marrakchi
De Juan Camilo Arosemena Serrato
De Albert Schwarz
De Juan Camilo Arosemena Serrato
De Francesca Arici
De Amine Marrakchi
