Examples of scrambling (cit) dynamics

scramblingDynamics.m

(* 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 *)
changeOfBasisUnitary = With[{\[Omega] = Exp[2 Pi I/3]},
    Table[
        Flatten @ KroneckerProduct[
            {1, \[Omega]^n, \[Omega]^(2 n)},
            {1, \[Omega]^m, \[Omega]^(2 m)}
        ],
        {n, {0, 1, 2}}, {m, {0, 1, 2}}
    ] / 3 // ArrayReshape[#, {9, 9}] & // Transpose
];
(* the following gives a permutation matix *)
Dot[
    ConjugateTranspose @ changeOfBasisUnitary,
    superScrambling2qutritsUnitary,
    changeOfBasisUnitary
] // MatrixForm // FullSimplify