A majorization relation for a sum of two tensor products of positive semidefinite operators

• URL: http://arxiv.org/abs/2607.07913v1
• Date: Wed, 08 Jul 2026 20:54:05 GMT
• Title: A majorization relation for a sum of two tensor products of positive semidefinite operators
• Abstract summary: We prove a separable version of Ky Fan's majorization relation for a sum of two operators that are each a tensor product of $n$ positive semidefinite operators.<n>We show that such a relation does not hold in general for sums of three or more tensor products of three or more positive semidefinite operators.
• Score: 0.42970700836450476
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We use linear programming to prove a separable version of Ky Fan's majorization relation for a sum of two operators that are each a tensor product of $n$ positive semidefinite operators. We give an example showing that such a relation does not hold in general for sums of three or more tensor products of three or more positive semidefinite operators.

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