JOURNAL ARTICLE

Equality condition for a matrix inequality with Kronecker product.

  • Published In: International Journal of Quantum Information, 2025, v. 23, n. 5. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Tan, Ziyue 3 of 3

Abstract

Quantum information theory has been greatly developed in the past decades, and many theoretical problems are related to matrix theory. We study the equality condition for a matrix inequality, K ⋅ rank( ∑ i = 1 K R i ⊗ S i ) ≥ rank( ∑ i = 1 K R i ⊗ S i T) , where R i 's are linearly independent matrices of the same size, and S i 's are linearly independent matrices of the same size. The inequality used to be a conjecture since 2013 and has recently been proven in the paper [Z. Song, L. Chen, Y. Sun and M. Hu, IEEE Trans. Inform. Theory69 (2023) 2385]. We study several cases such as that R i 's are column vectors and S i 's are of various sizes. It turns out that some cases never satisfy the equality condition. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Quantum Information. 2025/08, Vol. 23, Issue 5, p1
  • Document Type:Article
  • Subject Area:Political Science
  • Publication Date:2025
  • ISSN:0219-7499
  • DOI:10.1142/S0219749925500017
  • Accession Number:187102065
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