A new criterion and a special class of k-positive maps Dedicated to Professor Leiba Rodman

Jinchuan Hou; Chi Kwong Li; Yiu Tung Poon; Xiaofei Qi; Nung Sing Sze

doi:10.1016/j.laa.2014.02.008

A new criterion and a special class of k-positive maps Dedicated to Professor Leiba Rodman

Jinchuan Hou
, Chi Kwong Li
, Yiu Tung Poon
, Xiaofei Qi
, Nung Sing Sze

Research output: Journal article publication › Journal article › Academic research › peer-review

18 Citations (Scopus)

Abstract

We study k-positive maps on operators. We obtain a new criterion on k-positivity in terms of the k-numerical range, and use it to improve and refine some earlier results on k-positive maps related to the study of quantum information science. We also consider a special class of positive maps extending the construction of Choi on positive maps that are not completely positive. Some open questions on the decomposability of such maps are answered.

Original language	English
Pages (from-to)	51-69
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	470
DOIs	https://doi.org/10.1016/j.laa.2014.02.008
Publication status	Published - 1 Apr 2015

Keywords

k-numericalrange
k-positivemaps

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

More information

10.1016/j.laa.2014.02.008

Cite this

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abstract = "We study k-positive maps on operators. We obtain a new criterion on k-positivity in terms of the k-numerical range, and use it to improve and refine some earlier results on k-positive maps related to the study of quantum information science. We also consider a special class of positive maps extending the construction of Choi on positive maps that are not completely positive. Some open questions on the decomposability of such maps are answered.",

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AU - Hou, Jinchuan

AU - Li, Chi Kwong

AU - Poon, Yiu Tung

AU - Qi, Xiaofei

AU - Sze, Nung Sing

PY - 2015/4/1

Y1 - 2015/4/1

N2 - We study k-positive maps on operators. We obtain a new criterion on k-positivity in terms of the k-numerical range, and use it to improve and refine some earlier results on k-positive maps related to the study of quantum information science. We also consider a special class of positive maps extending the construction of Choi on positive maps that are not completely positive. Some open questions on the decomposability of such maps are answered.

AB - We study k-positive maps on operators. We obtain a new criterion on k-positivity in terms of the k-numerical range, and use it to improve and refine some earlier results on k-positive maps related to the study of quantum information science. We also consider a special class of positive maps extending the construction of Choi on positive maps that are not completely positive. Some open questions on the decomposability of such maps are answered.

KW - k-numericalrange

KW - k-positivemaps

UR - https://www.scopus.com/pages/publications/85027956463

U2 - 10.1016/j.laa.2014.02.008

DO - 10.1016/j.laa.2014.02.008

M3 - Journal article

SN - 0024-3795

VL - 470

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EP - 69

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A new criterion and a special class of k-positive maps Dedicated to Professor Leiba Rodman

Abstract

Keywords

ASJC Scopus subject areas

More information

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