Ky Fan majorization for binary tensor products

Abstract:We provide a short proof of a Ky Fan-type majorization relation for the singular values of a sum of binary tensor products of matrices. This generalizes Alhejji's result (arXiv:2410.18254) from two summands to arbitrary sums and from positive matrices to arbitrary matrices. As an application, we show a majorization relation between the singular values of a completely positive map and those of its Kraus operators.

Quantum Physics (quant-ph); Functional Analysis (math.FA)

arXiv:2607.27116 [quant-ph]

(or arXiv:2607.27116v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.27116 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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