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This paper presents a constructive algorithm for Kraus decomposition in infinite-dimensional Hilbert spaces, bridging the gap between abstract mathematical proofs and practical quantum process tomography. By generating Kraus operators sequentially with increasing sparsity, it ensures strong-operator topology convergence without relying on nonconstructive methods. This advancement is significant for quantum information theory, particularly in handling systems where finite-dimensional approximations are insufficient.
Existence of Kraus decomposition in infinite dimension via strongly-convergent direct process tomography
arXiv:2608.07207v2 Announce Type: replace 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.
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.
The equality in (7c) should have been an inclusion. This has been fixed, but it had no serious consequences. Proof of Lemma 1 has been rewritten, and explanation in Section IIIC expanded
arXiv:2608.07207 [quant-ph]
(or arXiv:2608.07207v2 [quant-ph] for this version)
From: Paul E. Lammert [view email] [v1] Fri, 7 Aug 2026 13:19:58 UTC (16 KB) [v2] Tue, 6 Oct 2026 23:03:50 UTC (18 KB)
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