镜像游戏的完美策略刻画

完美双答案量子非局部博弈的非交换零点定理

A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games

本文提出非交换零点定理，证明完美量子或交换算子策略的双答案非局部博弈均存在完美经典策略，并推广至无限维情形。

Perfect strategies for non-signalling games

We unify and consolidate various results about non-signall-ing games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a number of known facts in a variety of special cases. Among these families are {\it reflexive games,} which are characterised as the hardest non-signalling games that can be won using a given set of strategies. We introduce {\it imitation games,} in which the players display linked behaviour, and which contains as subclasses the classes of variable assignmen…

投影游戏的近完美策略近似迹性

Almost perfect strategies for projection games are approximately tracial

本文研究了投影游戏的近完美策略，证明在量子和交换算子模型中，近完美策略可转化为迹性策略，改进了约束系统游戏的近似结果。

Synchronicity for quantum non-local games

We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes. We define *-algebras and C*-algebras of concurrent classical-to-quantum and concurrent quantum non-local games, and algebraic versions of the orthogonal rank of a graph. We show that quantum homomorphisms of quantum graphs can be viewed as entanglement assisted classical homomorphisms of the graphs, and give …

模仿博弈的完美量子近似策略

Perfect Quantum Approximate Strategies for Imitation Games

研究模仿博弈的完美量子近似策略，证明其与两个通用C*-代数极小张量积上的双迹态等价，并探讨与von Neumann代数及顺从迹态的联系。

Algebras, Synchronous Games and Chromatic Numbers of Graphs

We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game, this leads to characterizations in terms of properties of an algebra of various quantum chromatic numbers that have been studied in the literature. This allows us to develop a correspondence between various chromatic numbers of a graph and ideals in this algebra which can then be approached via various Grobner basis methods.