 Selective phase rotation

For a unit vector $|\psi ⟩$ and real $\varphi$,multiplies the component parallel to $|\psi ⟩$ by $e^{i\varphi }$ and fixes its orthogonal complement. The case $\varphi =\pi$ is a reflection operator.

A reflection operator is a unitary involution that changes sign on one orthogonal subspace and fixes its orthogonal complement. For a unit vector $|\psi ⟩$, $I-2|\psi ⟩⟨\psi |$ reflects in the hyperplane perpendicular to $|\psi ⟩$.