a density matrix whose off-diagonal elements are all zero is “decohered”, and can be considered the classical limit of this. A decohered density matrix behaves exactly like a classical distribution, and follows classic Markovian dynamics;
I don’t think this bullet point is accurate. Any pure state will have all its off-diagonal elements be zero in a basis where that state is one of the basis vectors, but it’s not fair to say that any pure state “behaves exactly like a classical distribution”. I suppose it would be more accurate to say that a state whose off-diagonal entries are all zero in some basis will look classical with respect to dynamics and measurements in that basis, but that concept is hard to explain unless the idea of observables corresponding to Hermitian operators has already been explained.
I don’t think this bullet point is accurate. Any pure state will have all its off-diagonal elements be zero in a basis where that state is one of the basis vectors, but it’s not fair to say that any pure state “behaves exactly like a classical distribution”. I suppose it would be more accurate to say that a state whose off-diagonal entries are all zero in some basis will look classical with respect to dynamics and measurements in that basis, but that concept is hard to explain unless the idea of observables corresponding to Hermitian operators has already been explained.