Mixed Qubit Cannot Be Universally Broadcast

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 ${\rho }_s(\theta ,\omega ,\lambda )$ is regarded as constant in the fidelity. For the case of constant $\omega$, we establish the $1\to 2$ 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 $\lambda$ is the unique parameter in the fidelity. For general $N\to M$ broadcasting of mixed qubits, the situation is very different.

5 pages, Revtex

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Cited by in corpus (5)

• Quantum Cloning Machines and the Applications
• Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis
• Optimal Broadcasting of Mixed States
• Unified quantum no-go theorems and transforming of quantum states in a restricted set
• Quantum secure learning with classical samples