On a Tracial Version of Haemers Bound

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