1. The problem statement, all variables and given/known data Let q be a mixed state which we mix from pure states. What are the weights we must take for the pure states, respectively? Let us start the solution with the two-state system. 3. The attempt at a solution My problem is I can't decypher what the problem actually is, from my knowledge a mixed state is any combination of (assume there's a discrete collection of them) pure states summed with weights that add to 1 so at best we get a n-1 dimensional plane of solutions (for n pure states). So I think I'm seeing this problem incorrectly, could someone push me in the right direction?