Birkhoff's polytope and unistochastic matrices, N=3 and N=4

被引：51

作者：

Bengtsson, I ^{[1
]}

Ericsson, Å

Kus, M

Tadej, W

Zyczkowski, K

机构：

[1] Univ Stockholm, AlbaNova, S-10691 Stockholm, Sweden

[2] Polish Acad Sci, Cent Fizyki Teoret, PL-02668 Warsaw, Poland

[3] Cardinal Stefan Wyszynski Univ, Warsaw, Poland

[4] Jagiellonian Univ, Inst Fizyki Smoluchowskiego, PL-30059 Krakow, Poland

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2005年 / 259卷 / 02期

关键词：

D O I：

10.1007/s00220-005-1392-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The set of bistochastic or doubly stochastic N x N matrices is a convex set called Birkhoff's polytope, which 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.

引用

页码：307 / 324

页数：18

共 31 条

[1] ON THE RECONSTRUCTION OF A UNITARY MATRIX FROM ITS MODULI [J].