Is it possible to distinguish between pure and mixed states?

[PeterDonis]

Is it possible to prepare an ensemble of particles that are in some kind of Indeterminate spin state?

Others have given various ways of doing this; but none of these will give you what you said you wanted in Ensemble B, namely a "mixed" state. A mixed state is something different from what you are calling an "indeterminate" state. And the original quote you gave regarding the black hole information paradox was talking about mixed states (vs. pure states), not about indeterminate states (as opposed to determinate states).

If you still haven't picked up on my advice to consult a textbook and learn the technical meanings of all these terms you are using, do so. Once you have done so, please start a new thread if you still have questions about pure vs. mixed states. This thread is closed.