For all practical purposes, a density matrix indistinguis...

Classical probability distribution(as used in probability theory and philosophy of science): The traditional way of describing uncertainty using everyday odds—like saying a dice roll has a 1-in-6 chance of landing on each number.
Definite outcomes(as used in physics and logic): Results or states that are concrete and settled, as opposed to being uncertain or undefined.
Density matrix(as used in quantum mechanics): A mathematical tool physicists use to describe all the possible states a quantum system could be in and how likely each one is.
For all practical purposes(as used in philosophy of knowledge): In a way that works and matters for everyday life and decision-making, even if it might not be perfectly true in some abstract or theoretical sense.
Physically equivalent(as used in physics and philosophy of science): Two things that produce exactly the same observable results and outcomes, so for all practical purposes they behave identically.
Proper mixture(as used in quantum mechanics): A situation in quantum mechanics where a system is genuinely in one of several different definite states, but we don't know which one—like a coin that's already landed but we haven't looked yet.

2 topics

For all practical purposes, a density matrix indistinguishable from a proper mixture of definite outcomes is physically equivalent to a classical probability distribution over those outcomes.