= Two-outcome LOCC dilution of a Bell pair
{title2=$M_0=\operatorname{diag}(c,s),\quad M_1=\operatorname{diag}(s,c)$}
Let $c,s\geq0$ and $c^2+s^2=1$. Starting from the <Bell state> $(|00\rangle+|11\rangle)/\sqrt2$, Alice applies the <quantum measurement> with <Kraus operators> $M_0,M_1$ displayed above. Completeness follows from $M_0^\dagger M_0+M_1^\dagger M_1=I$. Each outcome has <probability> $1/2$. The normalized outputs are $c|00\rangle+s|11\rangle$ and $s|00\rangle+c|11\rangle$. Communicating the outcome allows both parties to apply a <Pauli X gate> in the second branch, making both outputs equal to the first. Thus this <LOCC> protocol deterministically converts one <Bell pair> into any two-<qubit> <pure state> with these <Schmidt coefficients>, after appropriate <local unitary operations>. It includes the <product state> endpoint without <postselection>.
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