**Symmetric minimal quantum tomography by successive measurements** - Amir Kalev

In this talk we consider the implementation of a symmetric
informationally complete probability-operator measurements (SIC POM)
in the Hilbert space of a d-level system by a two-step measurement
process: a diagonal-operator measurement with high-rank outcomes,
followed by a rank-1 measurement in a basis chosen in accordance with
the result of the first measurement. We find that any Heisenberg-Weyl
group-covariant SIC POM can be realized by such a sequence where the
second measurement is simply a measurement in the Fourier basis,
independent of the result of the first measurement. Furthermore, at
least for the particular cases studied, of dimension 2, 3, 4, and 8,
this scheme reveals an unexpected operational relation between
mutually unbiased bases and SIC POMs; the former are used to construct
the latter. As a laboratory application of the two-step measurement
process, we propose feasible optical experiments that would realize
SIC POMs in various dimensions.