Two-component gadget for transforming any two nonorthogonal polarization states into one another

We present an algorithm for transforming an arbitrary input polarization state into a nonorthogonal but otherwise arbitrary output polarization state, by using two quarter-wave retarders. Such an array reduces the number of retarders employed in the well-known Simon–Mukunda gadget, which consists of one half-wave and two quarter-wave retarders. The latter was designed to realize arbitrary SU(2)$\mathit{SU}(2)$ transformations on qubits. The gadget presented here accomplishes a related task, allowing to transforming an input qubit into a target qubit, by choosing a particular SU(2)$\mathit{SU}(2)$ transformation that is realizable with two quarter-wave plates.