= Deterministic two-qubit entanglement dilution
{title2=$|\Phi^+\rangle\longrightarrow u|00\rangle+v|11\rangle$}
For nonnegative $u,v$ with $u^2+v^2=1$, Alice applies <Kraus operators> $M_0=\operatorname{diag}(u,v)$ and $M_1=\operatorname{diag}(v,u)$ to one half of a <Bell state>. Their squared effects sum to the identity, and both outcomes have probability one half. The first branch is the target; the second becomes the target after both parties apply <Pauli X gates>. Sending the outcome by <classical communication> makes this exact deterministic <entanglement dilution>, rather than a postselected conversion.
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