Superpositions of unitary operators in quantum mechanics

We discuss the significance of superpositions of unitary operators in the formalism of quantum mechanics. We show that with this viewpoint, it can be demonstrated that one can observe a measurement with zero Ozawa uncertainty in a physically realisable feedback set-up which uses polarised photons coupled to spin. We derive a set of conditions under which a linear combination of unitary matrices is also a unitary matrix and confirm that the conditions are met by a realistic quantum gate.