A problem relating to positive linear maps on matrix algebras
type: Item
instance of: scholarly article
title: A problem relating to positive linear maps on matrix algebras
zbMATH Open document ID: 0534.15014
DOI: 10.1016/0034-4877(80)90083-X
published in: Reports on Mathematical Physics
publication date: 1980-01-01T00:00:00Z
review text: This paper deals with a problem which is solved in the commutative case but still unknown in the matrix cases. Namely, let X, Y, Z, Z' be density matrices. Does there exist a stochastic map (i.e. a linear, positivity- and trace-preserving one), say, L, such that \(X=L(Z)\), \(Y=L(Z')\), in the case that \(\| X-tY\|_ 1\leq \| Z-tZ'\|\), for all positive numbers t. The authors are able to find an affirmative answer in the 2\(\times 2\)-case.
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 3847582
zbMATH Keywords: density matrices
zbMATH Keywords: matrix algebras
zbMATH Keywords: stochastic map
author: Peter M. Alberti
author: Armin Uhlmann
reviewed by: Alfred Wehrl
MaRDI profile type: Publication
cites work: Q4189668
cites work: Subalgebras of \(C^ *\)-algebras
cites work: An “alternierende Verfahren” for general positive operators
cites work: Extreme Points of Some Convex Subsets of L 1 (0, 1)
cites work: Positive maps of low dimensional matrix algebras
full work available at URL: 0034-4877(80)90083-x
OpenAlex ID: W2125151656
description: scientific article; zbMATH DE number 3847582