High fidelity quantum cloning of two known nonorthogonal quantum states via weak measurement

We propose a scheme to enhance the fidelity of symmetric quantum cloning machine using a weak measurement. By adjusting the intensity of weak measurement parameter $p$, we obtain the copies with different optimal fidelity. Choosing proper value of $p$, we can obtain the perfect copies for initial qubits. In this paper, we focus on $1-2$ quantum cloning for two nonorthogonal states. Sets containing more than two linear independent states are also discussed briefly. Due to weak measurements being probabilistic, we obtain high fidelity at risk of probability. If the weak measurement successes, we do the following operations to obtain copies with high fidelity, otherwise, the cloning process fails and we need do nothing. From this perspective, the scheme we propose is economical for saving quantum resource and time, which may be very useful in quantum information processing.