Reply to Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'
- URL: http://arxiv.org/abs/2504.15576v3
- Date: Thu, 24 Apr 2025 05:59:31 GMT
- Title: Reply to Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'
- Abstract summary: We show that the number of complex Hadamard submatrices of order-two of any H2-reducible matrix is not 10,...,16,18.<n>We put forward some possible directions for further development.
- Score: 5.809735666368632
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Daniel McNulty et.al (2024 J. Phys. A: Math. Theor. submitted) voiced suspicions to the Lemma 11(v) Part 6 in Chen and Yu (2017 J. Phys. A: Math. Theor. 50 475304) and three theorems derived in later publications (Liang et al 2019 Quantum Inf. Process. 18 352; Liang et al 2019 Linear Multilinear Algebra 69 2908-25; Chen et al 2021 Quantum Inf. Process. 20 353). For these suspicions, we reprove that any complex Hadamard matrix of order-six whose number of real elements more than 22 does not belong to a set of four mutually unbiased bases. We show that the number of complex Hadamard submatrices of order-two of any H2-reducible matrix is not 10,...,16,18. We also put forward some possible directions for further development.
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