Binary Schmidt filter ($M_1=\mathrm{diag}(\sin \theta ,\cos \theta ),M_2=\mathrm{diag}(\cos \theta ,\sin \theta )$)

For a pure state with two descending squared Schmidt coefficients ${\lambda }_0\ge {\lambda }_1$, this quantum instrument acts in one party's Schmidt basis. The first outcome balances the two Schmidt amplitudes when $\tan \theta =\sqrt{{\lambda }_1/{\lambda }_0}$, with probability $2{\lambda }_0{\lambda }_1$. This is not the optimal unrestricted success probability $2{\lambda }_1$ in single-copy entanglement concentration. An embedding in a larger subsystem requires a POVM on the occupied support or a full-space completion.