Fig. 2: Circuit implementation of a single-basis rotation channel \({{\mathcal{E}}}_{{U}_{\psi }}\).
From: On the query complexity of unitary channel certification
The unitary operator Vψ maps the basis state \(\left\vert \psi \right\rangle\) to the computational basis state \({\left\vert 1\right\rangle }^{\otimes n}\). The controlled-rotation gate applies a phase shift of \(2{\sin }^{-1}(\varepsilon /2)\) to this computational basis component. As a result, the entire circuit behaves as a phase-shifting channel for the \(\left\vert \psi \right\rangle\) basis and as an identity channel for all other bases.
