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## Main Question or Discussion Point

Hi, I'm currently working on showing the relation of quantum fidelity:

The quantum “fidelity” between two pure states ρ1 = |ψ1⟩⟨ψ1| and ρ2 = |ψ2⟩⟨ψ2| is given by |⟨ψ1|ψ2⟩|^2.

Show that this quantity may be written as Tr(ρ1ρ2).

I've been following the wikipedia page on fidelity but can't understand it.

If I assume the statement is true and start from the Tr(ρ1ρ2) = Tr(|ψ1⟩⟨ψ1|ψ2⟩⟨ψ2|) I'm trying to find how I can reduce this, perhaps with summations to arrive at |⟨ψ1|ψ2⟩|^2 - can anyone suggest which direction to go in?

The quantum “fidelity” between two pure states ρ1 = |ψ1⟩⟨ψ1| and ρ2 = |ψ2⟩⟨ψ2| is given by |⟨ψ1|ψ2⟩|^2.

Show that this quantity may be written as Tr(ρ1ρ2).

I've been following the wikipedia page on fidelity but can't understand it.

If I assume the statement is true and start from the Tr(ρ1ρ2) = Tr(|ψ1⟩⟨ψ1|ψ2⟩⟨ψ2|) I'm trying to find how I can reduce this, perhaps with summations to arrive at |⟨ψ1|ψ2⟩|^2 - can anyone suggest which direction to go in?