Quantum measurements with prescribed symmetry
Abstract
We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As consequence, we provide a simple derivation of the maximal family of Symmetric Informationally Complete measurements (SIC)-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16 and (c) contextuality Kochen-Specker sets in dimension 3, 4 and 6, composed of 13, 18 and 21 vectors, respectively.
Cite
@article{arxiv.1704.04609,
title = {Quantum measurements with prescribed symmetry},
author = {W. Bruzda and D. Goyeneche and K. Życzkowski},
journal= {arXiv preprint arXiv:1704.04609},
year = {2017}
}
Comments
10 pages, 2 figures