Universal Asymmetric Quantum Cloning Revisited

This paper revisits the universal asymmetric $1 \to 2$ quantum cloning problem. We identify the symmetry properties of this optimisation problem, giving us access to the optimal quantum cloning map. Furthermore, we use the bipolar theorem, a famous method from convex analysis, to completely characterise the set of achievable single quantum clone qualities using the fidelity as our figure of merit; from this it is easier to give the optimal cloning map and to quantify the quality tradeoff in universal asymmetric quantum cloning. Additionally, it allows us to analytically specify the set of achievable single quantum clone qualities using a range of different figures of merit.