docs: def so4_to_magic_su2s(
          mat: np.ndarray,
          *,
          rtol: float = 1e-5,
          atol: float = 1e-8,
          check_preconditions: bool = True
  ) -> Tuple[np.ndarray, np.ndarray]:
      """Finds 2x2 special-unitaries A, B where mat = Mag.H @ kron(A, B) @ Mag.
  
      Mag is the magic basis matrix:
  
          1  0  0  i
          0  i  1  0
          0  i -1  0     (times sqrt(0.5) to normalize)
          1  0  0 -i
  
      Args:
          mat: A real 4x4 orthogonal matrix.
          rtol: Per-matrix-entry relative tolerance on equality.
          atol: Per-matrix-entry absolute tolerance on equality.
          check_preconditions: When set, the code verifies that the given
              matrix is from SO(4). Defaults to set.
  
      Returns:
          A pair (A, B) of matrices in SU(2) such that Mag.H @ kron(A, B) @ Mag
          is approximately equal to the given matrix.
  
      Raises:
          ValueError: Bad matrix.
          """
      if check_preconditions:
          if mat.shape != (4, 4) or not predicates.is_special_orthogonal(
                  mat, atol=atol, rtol=rtol):
              raise ValueError('mat must be 4x4 special orthogonal.')
  
      ab = combinators.dot(MAGIC, mat, MAGIC_CONJ_T)
      _, a, b = kron_factor_4x4_to_2x2s(ab)
  
      return a, b