Non-unitary transformations in quantum mechanics: An optical realization

Abstract

We show how to construct devices which implement non-unitary transformations on quantum systems with a certain probability of success. The first transforms two specified non-orthogonal states to orthogonal ones while the second can be used to enhance the entanglement of quantum states. The states themselves are composed of qubits which are realized as photons in the dual-rail representation, and these photons serve as the inputs to a six-port. One of the outputs is measured, and if a null result is obtained, the desired non-unitary transformation has been carried out. The transformation which takes non-orthogonal to orthogonal states is an optical realization of an optimal quantum measurement for distinguishing the two non-orthogonal states.