Mixed qubits cannot be universally broadcast
Lin Chen, Yi-Xin Chen · Physical Review A · 2007
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 ${\ensuremath{\rho}}_{s}(\ensuremath{\theta},\ensuremath{\omega},\ensuremath{\lambda})$ is regarded as constant in the fidelity. For the case of constant $\ensuremath{\omega}$, we establish the $1\ensuremath{\rightarrow}2$ optimal symmetric dependent cloner with a fidelity $1∕2$. It is also shown that the $1\ensuremath{\rightarrow}M$ optimal quantum cloning machine for pure qubits is also optimal for mixed qubits, when $\ensuremath{\lambda}$ is the unique parameter in the fidelity. For general $N\ensuremath{\rightarrow}M$ broadcasting of mixed qubits, the situation is very different.