Birkhoff's polytope and unistochastic matrices, N=3 and N=4
Combinatorics
2009-11-10 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff's polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.
Keywords
Cite
@article{arxiv.math/0402325,
title = {Birkhoff's polytope and unistochastic matrices, N=3 and N=4},
author = {Ingemar Bengtsson and Asa Ericsson and Marek Kus and Wojciech Tadej and Karol Zyczkowski},
journal= {arXiv preprint arXiv:math/0402325},
year = {2009}
}
Comments
30 pages, 4 figures