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arXiv · 2504.15576

Reply to Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'

Mengfan Liang·Lin Chen
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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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Mengfan Liang, Lin Chen. 2025-04-22. Reply to Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'. https://doi.org/10.1088/1751-8121%2Fadc885

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