  Let \Gamma be the convex set consisting of all marginal tracial states on the
tensor product B \otimes B of the algebra B of nxn matrices over the complex
numbers. We find necessary and sufficient conditions for such a state to be
extremal in \Gamma. We also give a characterization of those extreme points in
\Gamma which are pure states. We conjecture that all extremal marginal tracial
states are pure states.
