Is it possible, in principle, for an experiment to distinguish between an ensemble of pure states and an ensemble of mixed states? If so, how? In particular, I am thinking of an ensemble of particles whose spin has been measured, one at a time, on the "Vertical" axis. The ensemble consists of an equal number of spin-up particles and spin-down particles. Thus there should be no entanglement. This is the ensemble of pure states. The other ensemble has been prepared so that all particles are in a mixed state. Would a black hole consisting of one ensemble be different in any way from a black hole formed from the second ensemble?