  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.
