论文标题
量子到古典图同构游戏
The quantum-to-classical graph homomorphism game
论文作者
论文摘要
由非本地游戏和量子着色问题的动机，我们在量子图和经典图之间引入了图形同构游戏。该游戏自然是“量子古典游戏”，也就是说，这是一个非本地游戏，其中包括两个涉及量子问题和经典答案的玩家。该游戏概括了古典图之间的图形同构游戏。我们表明，游戏中各种量子模型中的获胜策略是对D. Stahlke引起的非交通图同构概念的类似物[44]。此外，我们在这种情况下提出了一个游戏代数，该游戏代数概括了J.W.给出的图形同构的游戏代数。 Helton，K。Meyer，V.I。 Paulsen和M. Satriano [22]。我们还展示了所有量子完整图的显式量子着色，这产生了一个令人惊讶的事实，即量子图的$ 4 $彩色游戏的代数始终是非平凡的，并扩展了[22]的结果。
Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a "quantum-classical game"--that is, a non-local game of two players involving quantum questions and classical answers. This game generalizes the graph homomorphism game between classical graphs. We show that winning strategies in the various quantum models for the game is an analogue of the notion of non-commutative graph homomorphisms due to D. Stahlke [44]. Moreover, we present a game algebra in this context that generalizes the game algebra for graph homomorphisms given by J.W. Helton, K. Meyer, V.I. Paulsen and M. Satriano [22]. We also demonstrate explicit quantum colorings of all quantum complete graphs, yielding the surprising fact that the algebra of the $4$-coloring game for a quantum graph is always non-trivial, extending a result of [22].
