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- W4200013016 abstract "It is conjectured that four mutually unbiased bases in dimension 6 do not exist in quantum information. The conjecture is equivalent to the nonexistence of some three 6×6 complex Hadamard matrices (CHMs) with Schmidt rank at least 3. We investigate the 6×6 CHM U of Schmidt rank 3 containing two nonintersecting identical 3×3 submatrices V, i.e. U=12[WVVX]. We show that such U exists, V, W, X have rank 2 or 3, and they have rank 2 at the same time. We construct the analytical expressions of U when V is, respectively, of rank 2, unitary and normal. We apply our results to the conjecture by showing that U with some normal V is not one of the three 6×6 CHMs." @default.
- W4200013016 created "2021-12-31" @default.
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- W4200013016 date "2021-12-16" @default.
- W4200013016 modified "2023-10-17" @default.
- W4200013016 title "On 6× 6 complex Hadamard matrices containing two nonintersecting identical 3× 3 submatrices" @default.
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- W4200013016 doi "https://doi.org/10.1080/03081087.2021.2014775" @default.
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