This question is from an example taken from Zurek 1991 (Decoherence and the Transition from Quantum to Classical). Start with a spin state of an electron, [tex]\Psi[/tex]= a|+> + b|-> Question 1: Why is this considered a pure state? I figured it would not be called "pure" since it is a superposition. I guess it is pure because it is not entangled, right? Now measure the electron with some quantum device, d. The states |d+> and |d-> span the Hilbert space of the device. The resulting correlated system can be described by a density matrix rho = a^2|+><+|d+><d+| + ab*|+><-|d+><d-| + a*b|-><+|d-><d+| + b^2|-><-|d-><d-| Question 2: Is this also a pure state? Why? Question 3: If I then write down the reduced density matrix, by setting the off-diagonal terms to zero, does this become a mixed state? Why?