Sandwich theorems and capacity bounds for non-commutative graphs

We define non-commutative versions of the vertex packing polytope, theta convex body and fractional polytope a graph, establish quantum version Sandwich Theorem Grötschel, Lovász Schrijver (1986) [7]. new number graph which lead to an upper bound zero-error capacity corresponding channel that can be genuinely better than one established by Duan, Severini Winter (2013) [5]. counterparts widely used classical parameters their interrelation.