Reply to Comment on ‘Product states and Schmidt rank of mutually unbiased bases in dimension six’
Year: 2025
Type: letter
Abstract: McNulty and Weigert (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 6 × 6 complex Hadamard matrix 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 2 × 2 complex Hadamard submatrices of any H 2-reducible matrix is not 10 , … , 16 , 18 . We also put forward some possible directions for further development.
Authors: Mengfan Liang, Lin Chen
Institution: Beihang University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409523987