Quantum channels, wavelets, dilations and representations of On

被引：58

作者：

Kribs, DW ^{[1
]}

机构：

[1] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2003年 / 46卷

关键词：

operator; completely positive map; quantum channel; orthogonal wavelet; isometric dilation; Cuntz algebra;

D O I：

10.1017/S0013091501000980

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the representations of the Cuntz C*-algebras O-n which arise in wavelet analysis and dilation theory can be classified through a simple analysis of completely positive maps on finite-dimensional space. Based on this analysis, we find an application in quantum information theory; namely, a structure theorem for the fixed-point set of a unital quantum channel. We also include some open problems motivated by this work.

引用

页码：421 / 433

页数：13

共 23 条

[11] Invariant subspaces and hyper-reflexivity for free semigroup algebras [J].

Davidson, KR ;

Pitts, DR .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1999, 78 :401-430

[12] MODELS FOR NON-COMMUTING OPERATORS [J].

FRAZHO, AE .

JOURNAL OF FUNCTIONAL ANALYSIS, 1982, 48 (01) :1-11

[13] TYPE I C'-ALGEBRAS [J].

GLIMM, J .

ANNALS OF MATHEMATICS, 1961, 73 (03) :572-&

[14]

HOLBROOK J, 2003, UNPUB GEN QUANTUM ER

[15] Wavelet representations and Fock space on positive matrices [J].

Jorgensen, PET ;

Kribs, DW .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 197 (02) :526-559

[16] Minimality of the data in wavelet filters [J].

Jorgensen, PET .

ADVANCES IN MATHEMATICS, 2001, 159 (02) :143-228

[17] Additivity for unital qubit channels [J].

King, C .

JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (10) :4641-4653

[18] GENERAL STATE CHANGES IN QUANTUM THEORY [J].

KRAUS, K .

ANNALS OF PHYSICS, 1971, 64 (02) :311-&

[19]

Nielsen M., 2000, CAMBRIDGE SERIES INF

[20]

PAULSEN V. I., 1986, Completely bounded maps and dilations

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