Given density operators $\rho_1$ and $\rho_2$ and a pure quantum state $|\psi>$. It is promised that $|\psi>$ is in only one of the given density operators. How to find which density operator $|\psi>$ belongs to?
2026-04-05 19:37:09.1775417829
Distance between a density operator and a pure quantum state.
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I suppose that what you are claiming is that $\langle\psi|\rho_i|\psi\rangle\neq 0$ for just one $i\in\{1,2\}$. Hence the criterion you are looking for.