Thank you very much for your clear explanation, I understand your point.
However, in a strictly mathematical sense, ##\rho(1)## and ##\rho(2)## are quantum states, in the sense that they are density matrices in ##H_1## and ##H_2##. So the question "are they necessarily mixed" (is...
I'm an undergrad in physics, and have been asking myself the following question recently. Suppose you have a pure quantum state p (von neumann entropy=0), made of 2 sub-states p1 and p2 that are entangled. Because they are entangled, p \neq p1 x p2. Hence the entanglement entropy of p (=0) is...