Understanding Christensen-Sinclair factorization via semidefinite programming

TL;DR

This paper demonstrates that the Christensen-Sinclair factorization theorem in finite-dimensional Hilbert spaces can be derived from strong duality in semidefinite programming, offering a simple proof and an efficient computational method.

Contribution

It establishes a novel connection between Christensen-Sinclair factorization and semidefinite programming duality, providing both theoretical insight and practical algorithms.

Findings

Proof of Christensen-Sinclair factorization via SDP duality

Elementary proof simplifies understanding of the theorem

Efficient algorithm for computing the factorization

Abstract

We show that the Christensen-Sinclair factorization theorem, when the underlying Hilbert spaces are finite dimensional, is an instance of strong duality of semidefinite programming. This gives an elementary proof of the result and also provides an efficient algorithm to compute the Christensen-Sinclair factorization.