The Kirchberg–Wassermann operator system is unique

In 1998, Kirchberg and Wassermann constructed a separable nuclear operator system with the property that the canonical unital ⁎-homomorphism from the maximal C*-algebra onto the C*-envelope is injective. We show that such an operator system is unique, and completely order isomorphic to the operator system associated with the noncommutative Poulsen simplex.