Comparing quantum cloning: A Fisher-information perspective
Hongting Song, Shunlong Luo, Nan Li, Lina Chang · Physical Review A · 2013
Perfect cloning of an unknown quantum state is impossible. Approximate cloning, which is optimal in various senses, has been found in many cases. Paradigmatic examples are Wootters-Zurek cloning and universal cloning. These cloning machines aim at optimal cloning of the full quantum states. However, in practice, what is important and relevant may only involve partial information in quantum states, rather than quantum states themselves. For example, signals are often encoded as parameters in quantum states, whose information content is well synthesized by quantum Fisher information. This raises the basic issue of evaluating the information transferring capability (e.g., distributing quantum Fisher information) of quantum cloning. We assess and compare Wootters-Zurek cloning and universal cloning from this perspective and show that, on average, Wootters-Zurek cloning performs better than universal cloning for the phase (as well as amplitude) parameter, although they are incomparable individually, and universal cloning has many advantages over Wootters-Zurek cloning in other contexts. Physical insights and related issues are further discussed.