I would like to rotate my $|\Psi\rangle$ state towards $|1\rangle$: $$ |\Psi\rangle= a|0\rangle + b|1\rangle \ \rightarrow \ |\Psi'\rangle= a'|0\rangle + b'|1\rangle$$ with $|a'| < |a|$, $|b'| > |b|$ and without prior knowledge of $a$, $b$.
I think a way to do it is to do a partial swap with an ancilla: $$ |\Psi\rangle|1\rangle_a \ \rightarrow \ |\Psi'\rangle|\phi\rangle_a $$
A criteria is that the strength of the rotation is parametrized $U(\theta)$. What happens to the ancilla $|\phi\rangle_a$ does not matter.
Is there something like a partial swap?