Mixed qubits cannot be universally broadcast

We show that no universal quantum cloning machine exists that can broadcast an arbitrary mixed qubit with a constant fidelity. Based on this result, we investigate the dependent quantum cloner in the sense that some parameter of the input qubit ₒ (, , ) is regarded as constant in the fidelity. For the case of constant, we establish the 12 optimal symmetric dependent cloner with a fidelity 1∕2. It is also shown that the 1 optimal quantum cloning machine for pure qubits is also optimal for mixed qubits, when is the unique parameter in the fidelity. For general N broadcasting of mixed qubits, the situation is very different.