Construction of all general symmetric informationally complete measurements
Quantum Physics
2014-08-15 v3 Information Theory
Mathematical Physics
math.IT
math.MP
Abstract
We construct the set of all general (i.e. not necessarily rank 1) symmetric informationally complete (SIC) positive operator valued measures (POVMs). In particular, we show that any orthonormal basis of a real vector space of dimension d^2-1 corresponds to some general SIC POVM and vice versa. Our constructed set of all general SIC-POVMs contains weak SIC-POVMs for which each POVM element can be made arbitrarily close to a multiple times the identity. On the other hand, it remains open if for all finite dimensions our constructed family contains a rank 1 SIC-POVM.
Keywords
Cite
@article{arxiv.1305.6545,
title = {Construction of all general symmetric informationally complete measurements},
author = {Amir Kalev and Gilad Gour},
journal= {arXiv preprint arXiv:1305.6545},
year = {2014}
}
Comments
8 pages, 1 figure