A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries

被引：0

作者：

Chruscinski, Dariusz ^{[1
]}

Bhattacharya, Bihalan ^{[1
]}

机构：

[1] Nicolaus Copernicus Univ, Inst Phys, Fac Phys Astron & Informat, Grudziadzka 5-7, PL-87100 Torun, Poland

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2024年 / 57卷 / 39期

关键词：

Schwarz inequality; positive maps; completely positive maps; Pauli channels; RELATIVE ENTROPY; QUANTUM; GENERATORS;

D O I：

10.1088/1751-8121/ad75d6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A class of unital qubit maps displaying diagonal unitary and orthogonal symmetries is analyzed. Such maps have already found a lot applications in quantum information theory. We provide a complete characterization of this class of maps showing intricate relation between positivity, operator Schwarz inequality, and complete positivity. Finally, it is shown how to generalize the entire picture beyond unital case (so called generalized Schwarz maps). Interestingly, the first example of Schwarz but not completely positive map found by Choi belongs to our class. As a case study we provide a full characterization of Pauli maps. Our analysis leads to generalization of seminal Fujiwara-Algoet conditions for Pauli quantum channels.

引用

页数：19

共 21 条

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[18] Orthogonal Polynomial Duality and Unitary Symmetries of Multi-species ASEP(q,θ) and Higher-Spin Vertex Models via ∗-Bialgebra Structure of Higher Rank Quantum Groups
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[19] A NOTE ON A SPECIAL CLASS OF UNITARY REPRESENTATION OF INHOMOGENEOUS GROUP U-12XT143 WHICH UNDERLIES SALAMS MODEL OF RELATIVISTIC SU6 SYMMETRIES
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[20] A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbf{SO}(n)$\end{document}
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