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arXiv · 2608.07207

Existence of Kraus decomposition in infinite dimension via strongly-convergent direct process tomography

Paul E. Lammert
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Abstract

An algorithm is presented for Kraus decomposition of a completely positive operator over separable (countably-infinite-dimensional) Hilbert spaces, together with an elementary proof that the generated sum convergences in strong-operator topology. This improves on the standard, nonconstructive, proof by fusing the abstract problem with practical process tomography. Kraus operators are generated one-by-one, each having one more guaranteed zero matrix entry than the previous one. In this way, the stream of outputs of the algorithm provides a coherent family of Kraus decompositions of restrictions of the target CP map to ever-larger subspaces.

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Paul E. Lammert. 2026-08-07. Existence of Kraus decomposition in infinite dimension via strongly-convergent direct process tomography. https://arxiv.org/abs/2608.07207

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