= Concurrence scaling under invertible local filters
{title2=$C(\rho')=\frac{|\det A\det B|}{p}C(\rho)$}
For $\rho'=(A\otimes B)\rho(A^\dagger\otimes B^\dagger)/p$, with invertible $A,B$, a pure coefficient matrix transforms as $M\mapsto AMB^{\mathsf T}$. Its unnormalized determinant is multiplied by $\det A\det B$. The invertible filter bijects pure decompositions before and after conditioning, with branch weights rescaled by their success probabilities. Taking both infima in the <convex roof extension> gives the displayed exact scaling. If either filter has rank one, the retained state is separable across that party.
Back to article page
