We extend upper bounds on the quantum independence number and the quantum Shannon capacity of graphs to their counterparts in the commuting operator model. We introduce a von Neumann algebraic generalization of the fractional Haemers bound (over $\mathbb{C}$) and prove that the generalization upper bounds the commuting quantum independence number. We call our bound the tracial Haemers bound, and we prove that it is multiplicative with respect to the strong product. In particular, this makes it an upper bound on the Shannon capacity. The tracial Haemers bound is incomparable with the Lov\'asz theta function, another well-known upper bound on the Shannon capacity. We show that separating the tracial and fractional Haemers bounds would refute Connes' embedding conjecture. Along the way, we prove that the tracial rank and tracial Haemers bound are elements of the (commuting quantum) asymptotic spectrum of graphs (Zuiddam, Combinatorica, 2019). We also show that the inertia bound (an upper bound on the quantum independence number) upper bounds the commuting quantum independence number.

翻译：我们将量子独立数的上限和香农的量子图的量子容量的量子独立数和香农的量子图的量子能力扩大到通勤操作模型中的对应方。 我们引入了对分数海默斯约束的 von Neumann 代数法的概括化概括( 超过 $mathbb{C} 美元), 并证明一般化的上限将否定交量独立数。 我们称我们被约束的量子独立数是强产产品的倍数。 特别是, 这使得它成为香农能力的一个上限。 种族海默斯捆绑与Lov\'asz theta函数是无法比较的, 这是香农产能力上另一个众所周知的上限。 我们表明, 将种族和分数界限分开将反驳Connes的嵌入式指针。 顺便说, 我们证明, 种族等级和种族的量子捆绑是( commodam, Commonatorica, 2019) 图形(Zuiddaddam ) 的亚质独立。 我们还显示, 上定了量独立。