= Single-copy entanglement concentration
{title2=$p_{\max}=2\lambda_{\min}$}
For one pure rank-two entangled state with descending squared <Schmidt coefficients> $(\lambda_0,\lambda_1)$, the success operator $F=\operatorname{diag}(\sqrt{\lambda_1/\lambda_0},1)$ gives a <Bell pair> with probability $2\lambda_1$. The complementary operator $\sqrt{I-F^\dagger F}$ makes a valid <quantum instrument>. Optimality follows from the <Schmidt-tail entanglement monotone>: a successful Bell branch has smallest weight $1/2$, so its probability cannot exceed $2\lambda_1$. Failure branches have nonnegative monotone and cannot loosen this bound.
Back to article page
