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)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)SU(2) transformation that is realizable with two quarter-wave plates.

► Given two polarization states, we transform one into the other by using two quarter-wave plates.
► An algorithm outputs the wave-platesʼ setting for any two nonorthogonal states.
► The algorithm complements Simon–Mukundaʼs three-component gadget for SU(2)SU(2) transformations.
► Our approach can be applied to other realizations of qubits.