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Reply to Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'
Mengfan Liang, Lin Chen
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 theore…
Order-six CHMs containing exactly three distinct elements
Yanzu Huang, Mengfan Liang, Lin Chen
Complex Hadamard matrices (CHMs) are intimately related to the number of distinct matrix elements. We investigate CHMs containing exactly three distinct elements, which is also the…
Eigenvalues and eigenvectors of complex Hadamard matrices
Mengfan Liang, Lin Chen
Characterizing the complex Hadamard matrices (CHMs) is an open problem in linear algebra and quantum information. In this paper, we investigate the eigenvalues and eige…
-reducible matrices in six-dimensional mutually unbiased bases
Xiaoyu Chen, Mengfan Liang, Mengyao Hu +1
Finding four six-dimensional mutually unbiased bases (MUBs) containing the identity matrix is a long-standing open problem in quantum information. We show that if they exist, then…