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arXiv · 2603.19444

The Choi-Cholesky algorithm for completely positive maps

Raj Dahya
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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.

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Raj Dahya. 2026-03-19. The Choi-Cholesky algorithm for completely positive maps. https://arxiv.org/abs/2603.19444

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