= Single-copy Werner filtering cannot increase concurrence
{title2=$C(\rho_{\rm retained})\leq C(W_F)$}
Combine the <single-copy Werner filtering normalization bound> with <concurrence scaling under invertible local filters>. Every complete classical record of <local operations and classical communication> has a product filter $A\otimes B$; singular branches are separable. Thus every retained branch has <concurrence> at most that of the input. Coarse-graining successful records preserves the bound by convexity. Since <concurrence of a two-qubit Werner state> increases strictly with $F$, no successful single-copy protocol can output a Werner state with larger $F$. Several input copies permit collective distillation and are outside this statement.
Back to article page
