PreprintCC BY 4.0arXiv
Existence of Kraus decomposition in infinite dimension via strongly-convergent direct process tomography
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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BibTeX
@misc{lammert2026existence,
title = {{Existence of Kraus decomposition in infinite dimension via strongly-convergent direct process tomography}},
author = {Paul E. Lammert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.07207},
eprint = {2608.07207},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07207},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Existence of Kraus decomposition in infinite dimension via strongly-convergent direct process tomography
AU - Paul E. Lammert
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2608.07207
UR - https://arxiv.org/abs/2608.07207
AB - 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.
ER -