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From John Preskill's quantum computation & quantum information lecture notes(chapter 5)

If a pure state is drawn randomly from the ensemble{|φ_{x}〉,p_{x}}, so that the density matrix is ρ = ∑p_{x}|φ_{x}〉<φ_{x}|

Then, H(X)≥S(ρ)

where H stands for Shannon entropy of probability {p_{x}} and S stands for Von Neumann entropy.

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# Proof of "Entropy of preparation" in Von Neumann entropy

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