Instytut Matematyczny PAN, 2014. We show that the space of tracial quantum symmetric states of an arbitrary unital C-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital C-algebra free product of A with itself infinitely many times. We also show that the extreme points of this simplex are dense, making it the Poulsen simplex when A is separable and nontrivial. In the course of the proof we characterize the centers of certain tracial amalgamated free product C-algebras.
