Analysis and Synthesis of Minimal Informationally Complete Quantum Measurements
John B. DeBrota, Christopher A. Fuchs, Blake C. Stacey · arXiv (Cornell University) · 2018
Minimal Informationally Complete quantum measurements, or MICs, illuminate the structure of quantum theory and how it departs from the classical. We establish general properties of MICs, explore constructions of several classes of them, and further develop the theory of MIC Gram matrices. These Gram matrices turn out to be a rich subject of inquiry, relating linear algebra, number theory and probability. This work provides further context to the discovery that the symmetric informationally complete quantum measurements (SICs) are in many ways optimal among MICs. In a deep sense, the ideal measurements of quantum physics are not orthogonal bases.