Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0005004

A Characterization of Completely-Positive Trace-Preserving Maps on 2x2 Matrices

Mary Beth Ruskai, Elisabeth M. Werner, Stanisław J. Szarek

Published Apr 29, 2000• 1 citation
arXivHTMLPDF

Abstract

This paper has been superseded by quant-ph/0101003.
DOI
10.48550/arxiv.quant-ph/0005004

Related papers

An analysis of completely-positive trace-preserving maps on M2

Mary Beth Ruskai, Stanisław J. Szarek, Elisabeth M. Werner

Linear Algebra and its Applications•May 1, 2002•353 citations

Characterizations of completely positive trace preserving majorants

Mohsen Kian, M. Rostamian Delavar, Mario Krnić

Linear Algebra and its Applications•Mar 3, 2026•0 citations

An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices

Mary Beth Ruskai, Stanisław J. Szarek, Elisabeth M. Werner

We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non-unital extreme points which can be characterized as having exactly two images on the Bloch sphere. We also discuss a number of related issues about the images and the geometry of the set of stochastic maps, and show that any stochastic map on 2x2 matrices can be written as a convex combination of two "generalized" extreme points.

arXiv:quant-ph/0101003•Dec 31, 2000•21 citations

Universal bound on the eigenvalues of 2-positive trace-preserving maps

Frederik vom Ende, Dariusz Chruściński, Gen Kimura +1 more

arXiv:2506.02145•Linear Algebra and its Applications•Oct 24, 2025•0 citations

New multiplicativity results for qubit maps

Christopher King, Nilufer Koldan

Let Phi be a trace-preserving, positivity-preserving linear map on the algebra of complex 2x2 matrices, and let Omega be any finite-dimensional completely positive map. For p=2 and for p >= 4, we prove that the maximal p-norm of the product map (Phi \\otimes Omega) is the product of the maximal p-norms of Phi and Omega. Restricting Phi to the class of completely positive maps, this settles the multiplicativity question for all qubit channels in the range of values p >= 4.

•Dec 21, 2005•9 citations

A problem relating to positive linear maps on matrix algebras

Peter M. Alberti, Armin Uhlmann

Reports on Mathematical Physics•Oct 1, 1980•73 citations
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non-unital extreme points which can be characterized as having exactly two images on the Bloch sphere. We also discuss a number of related issues about the images and the geometry of the set of stochastic maps, and show that any stochastic map on 2x2 matrices can be written as a convex combination of two "generalized" extreme points.