= Pure-state norm distance
{title2=$d_2(\psi,\phi)=\||\psi\rangle-|\phi\rangle\|_2$}
The <Euclidean norm> distance between normalized <pure state> vector representatives in a common <Hilbert space>. Its square is $2-2\operatorname{Re}\langle\psi|\phi\rangle$. If vectors differing by a <global phase> are identified, minimize over that phase to obtain $\sqrt{2-2|\langle\psi|\phi\rangle|}$. This is a different distance convention from <trace distance> or one minus <squared quantum fidelity>; stating the convention is necessary when defining $\varepsilon$-closeness.
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