| Abstract: | We consider the realization of a symmetric informationally-complete probability operator measurement (SIC POM) in d-dimensional Hilbert space through a succession of two measurements. The measurements are taken to be in a specific form. The first one is composed of projectors onto the computational basis mixed with the identity operator, while the second measurement is a projective measurement, which depends on the actual outcome of the first one. Surprisingly, this formulation reveals a general operational relation between unbiased bases and SIC POMs: The former is used to construct the latter. We study in particular such a realization in 2, 3, and 4-dimensional Hilbert space. We show that, for these dimensions, all group covariant SIC POMs could be realized with this specific form for the measurements. Furthermore, based on this scheme we propose a feasible experiment to realize the SIC POM for a 2-qubit system. |
