Symbolic integration with respect to the Haar measure on the unitary groups

被引：74

作者：

Puchala, Z. ^{[1
]}

Miszczak, J. A. ^{[1
]}

机构：

[1] Polish Acad Sci, Inst Theoret & Appl Informat, 5 Baltycka Str, PL-44100 Gliwice, Poland

来源：

BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES | 2017年 / 65卷 / 01期

关键词：

unitary group; Haar measure; circular unitary ensemble; symbolic integration;

D O I：

10.1515/bpasts-2017-0003

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of special cases which can be used to optimize the calculation speed for some classes of integrals. We also provide some examples of usage of the presented package.

引用

页码：21 / 27

页数：7

共 15 条

[1]

[Anonymous], 1981, ENCY MATH ITS APPL

[2] The computational complexity of rules for the character table of Sn [J].

Bernstein, D .

JOURNAL OF SYMBOLIC COMPUTATION, 2004, 37 (06) :727-748

[3] Integration with respect to the Haar measure on unitary, orthogonal and symplectic group [J].

Collins, B ;

Sniady, P .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 264 (03) :773-795

[4]

Donati-Martin C., 2010, ARXIV10071366

[5] Numerical shadow and geometry of quantum states [J].

Dunkl, Charles F. ;

Gawron, Piotr ;

Holbrook, John A. ;

Miszczak, Jaroslaw A. ;

Puchala, Zbigniew ;

Zyczkowski, Karol .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (33)

[6] Numerical shadows: Measures and densities on the numerical range [J].

Dunkl, Charles F. ;

Gawron, Piotr ;

Holbrook, John A. ;

Puchala, Zbigniew ;

Zyczkowski, Karol .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (09) :2042-2080

[7] Minimal Renyi-Ingarden-Urbanik Entropy of Multipartite Quantum States [J].

Enriquez, Marco ;

Puchala, Zbigniew ;

Zyczkowski, Karol .

ENTROPY, 2015, 17 (07) :5063-5084

[8]

Fulton W., 1991, GRADUATE TEXTS MATH

[9]

Hiai F., 2006, AM MATH SOC, V77

[10] Generating and using truly random quantum states in Mathematica [J].

Miszczak, Jaroslaw Adam .

COMPUTER PHYSICS COMMUNICATIONS, 2012, 183 (01) :118-124

← 1 2 →