OAI/Analysis/MutuallyUnbiased/Cubic/CubicExclusion.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

1. def OAI.MUB6.enumerateThree line 12
2. theorem OAI.MUB6.sum_enumerateThree line 15
3. theorem OAI.MUB6.no_hadamard_orthogonal_restrictions line 20
4. theorem OAI.MUB6.cubic_block_cross_orthogonal line 48
5. theorem OAI.MUB6.dephased_hadamard_cubes_one line 78

   Source documentation

   An arbitrary dephased complex Hadamard matrix whose entrywise square is Hadamard has only cube roots of unity as entries.

   theorem dephased_hadamard_cubes_one {H : CMatrix} (hH : IsHadamard H)
       (hH2 : IsHadamard (fun i j => H i j ^ 2))
       (h0row : ∀ j, H 0 j = 1) (h0col : ∀ i, H i 0 = 1) :
       ∀ i j, H i j ^ 3 = 1 := by
   …

   Mentions: OAI.MUB6.CMatrix, OAI.MUB6.IsHadamard