def METHOD_NAME(
    self, spin: Fraction | int
) -> tuple[SparsePauliOp, SparsePauliOp, SparsePauliOp, SparsePauliOp]:
    """The logarithmic encoding.
    Args:
        spin: Positive half-integer (integer or half-odd-integer) that represents spin.
    Returns:
        A tuple containing four SparsePauliOp.
    """
    spin_op_encoding: list[SparsePauliOp] = []
    dspin = int(2 * spin + 1)
    num_qubits = int(np.ceil(np.log2(dspin)))
    # Get the spin matrices
    spin_matrices = [
        SpinOp.x(spin).to_matrix(),
        SpinOp.y(spin).to_matrix(),
        SpinOp.z(spin).to_matrix(),
        np.eye(dspin),
    ]
    # Embed the spin matrices in a larger matrix of size 2**num_qubits x 2**num_qubits
    embedded_spin_matrices = [
        self._embed_matrix(matrix, num_qubits) for matrix in spin_matrices
    ]
    # Generate operators from these embedded spin matrices
    embedded_operators = [Operator(matrix) for matrix in embedded_spin_matrices]
    for op in embedded_operators:
        op = SparsePauliOp.from_operator(op)
        op.chop()
        spin_op_encoding.append(op)
    return tuple(spin_op_encoding)  # type: ignore