lucainnocenti

generatePair[pauliIndices_List, tuple_List] := {
   BitXor[
    ReplaceAll[
     pauliIndices, {3 -> 0, 2 -> 1}
     ],
    tuple
    ],
   (-1)^Total@tuple[[Flatten@Position[pauliIndices, 2 | 3]]] 
   };

lucainnocenti

(* this one gives maximally negative tripartite *)
superScrambling2qutritsUnitary := Table[
    Normal @ Flatten @ KroneckerProduct[
        SparseArray[{Mod[i + j, 3] + 1 -> 1}, 3],
        SparseArray[{Mod[i - j, 3] + 1 -> 1}, 3]
    ],
    {i, {0, 1, 2}}, {j, {0, 1, 2}}
] // ArrayReshape[#, {9, 9}] & // Transpose;

(* unitary changing local bases to Fourier bases *)