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Mixed Qubit Cannot Be Universally Broadcast

Lin Chen·Yi-Xin Chen
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Abstract

We show that there does not exist any universal quantum cloning machine 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 $ρ_s(θ,ω,λ)$ is regarded as constant in the fidelity. For the case of constant $ω$, we establish the $1\to2$ optimal symmetric dependent cloner with a fidelity 1/2. It is also shown that the $1\to M$ optimal quantum cloning machine for pure qubits is also optimal for mixed qubits, when $λ$ is the unique parameter in the fidelity. For general $N\to M$ broadcasting of mixed qubits, the situation is very different.

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Lin Chen, Yi-Xin Chen. 2006-12-25. Mixed Qubit Cannot Be Universally Broadcast. https://doi.org/10.1103/physreva.75.062322

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