Superpositions of unitary operators in quantum mechanics

Abstract

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.

Causality relations and hidden variable theories for the Mermin-Peres square

“…The discussion of quantum fluctuations and contextuality is clearly linked to the measurement problem, since several measurement theories in the literature suggest that these fluctuations represent a dynamical randomness [14,15]. Quantum contextuality enters here because by contextuality the different possible results which we observe in different measurements come from the same randomness, but they appear as different sets of possibilities depending on the measurement dynamics.…”

A possible solution to the which-way problem of quantum interference

“…The effects of local polarization rotations merely confirm that there is a correlation between the presence of each particle in the paths and the measurement outcome p of an interference measurement. Within the framework of the theory, this peculiar dependence of path presence on the outcomes p is possible because the quantum interferences between the two local polarization rotations result in a total change of the polarization that is fundamentally different from the two local rotations [23,24]. As explained above, this total change of the polarization cannot be explained in terms of a statistical distribution of the local rotation angles.…”