The Choi-Cholesky algorithm for completely positive maps
Functional Analysis
2026-04-07 v2 Mathematical Physics
math.MP
Abstract
We establish explicit means via which natural dilations of completely positive (CP) maps can be constructed \`a la Kraus's IInd representation theorem. To obtain this, we rely on the Choi-Jamio{\l}kowski correspondence and develop a Cholesky algorithm for bi-partite systems. This enables a canonical construction of adjoint actions which recover the behaviour of the original CP-maps. Our results hold under separability assumptions and the requirement that the maps are completely bounded and preserve the subideal of finite rank operators.
Keywords
Cite
@article{arxiv.2603.19444,
title = {The Choi-Cholesky algorithm for completely positive maps},
author = {Raj Dahya},
journal= {arXiv preprint arXiv:2603.19444},
year = {2026}
}
Comments
Added Remarks 1.4 (statement of related works), 2.13 (coherence of recursive construction); Minor adjustments to text; added reference to code base