  This letter reports a novel application of game theory to quantum
informational processes which can be used to optimally classify data generated
by these processes. To this end, the notion of simultaneously distinguishing a
pure quantum state, generated by a quantum informational process, from its
constituent observable states optimally - given the constraint of these
observables being orthogonal to each other, is first introduced. This problem
is solved via a non-cooperative game model and the affiliated solution concept
of Nash equilibrium. The notion of Nash equilibrium quantum states is
introduced and used to classify quantum data optimally.
