Pure and mixed states Sample Clauses

Pure and mixed states. Definition 7 If we can write a state in the form ρ = |ψ)(ψ| then Tr(ρ2) = 1 and we call the state pure. If i > 1 in (B.6) we call the state mixed and Tr(ρ2) < 1. Let |ψ) be a state vector of our system. Then Tr(ρ2) = Tr(|φ)(φ|φ)(φ|) = Tr(|φ)(φ|) = (φ|φ) = 1 where we used the normalization condition in equality two. If the state is not pure we cannot write it in the state vector form. Instead we have: ρ =
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