Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897734 | Linear Algebra and its Applications | 2018 | 16 Pages |
Abstract
In this paper, we present a parametric family of linear maps Φα,β,n:Mn(C)âMn2(C) and study the properties of positivity, completely positivity, decomposability etc. We determine values of parameters α and β for which the family of maps Φα,β,n is positive for any natural number nâ¥3. We focus on the case of n=3, that is, Φα,β,3 and study the properties of 2-positivity, completely positivity and decomposability. In particular, we give values of parameters α and β for which the family of maps Φα,β,3 is 2-positive and not completely positive.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Benoît Collins, Hiroyuki Osaka, Gunjan Sapra,