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"Symmetric minimal quantum tomography by successive measurements"

Amir Kalev
Centre for Quantum Technologies
National University of Singapore


We shall 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.

Friday, October 19, 2012
IQSE 578, 2:00 p.m.
Mitchell Physics Building

Department of Physics and Astronomy
Texas A&M University

(Coffee and Cookies to be served at 1:45 p.m.)

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