全局渐近克隆是状态估计吗？
Is global asymptotic cloning state estimation?
摘要：
我们提出的问题是，在单拷贝水平上有效的量子克隆和量子态估计之间的渐近等价性，当所有的拷贝被联合检查时，是否仍然成立。对于N-to-M克隆器，我们考虑M个输出系统的状态和M个理想拷贝的状态之间的整体保真度，并且我们询问在大M的限制下，测量和准备协议是否可以达到最佳保真度。为了直观地理解一般问题，我们分析了两个具体的例子：i）克隆Bloch球赤道上的量子比特态和ii）克隆两个量子比特的最大纠缠态。在第一种情况下，我们证明了在大M的限制下，最优测量和准备保真度收敛于最优克隆器的保真度。在第二种情况下，我们限制我们的注意力经济的协变克隆，并再次，我们表现出一个测量和准备协议，实现渐近的最佳保真度。非常违反直觉的是，在这两种情况下，为了最大化整体保真度而必须准备的最佳状态不是对应于M个相同副本的产品状态，而是合适的M-partite纠缠态：简单的协议，其中一个估计输入状态并重新准备M个相同的估计状态副本是严格次优的，即使在渐近极限。
英文摘要：
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at single-copy level, still holds when all the copies are examined jointly. For an N-to-M cloner, we consider the overall fidelity between the state of the M output systems and the state of M ideal copies, and we ask whether the optimal fidelity is attained by a measure-and- prepare protocol in the limit of large M. In order to gain intuition into the general problem, we analyze two concrete examples: i) cloning qubit states on the equator of the Bloch sphere and ii) cloning two-qubit maximally entangled states. In the first case, we show that the optimal measure-and- prepare fidelity converges to the fidelity of the optimal cloner in the limit of large M. In the second case, we restrict our attention to economical covariant cloners, and again, we exhibit a measure- and-prepare protocol that achieves asymptotically the optimal fidelity. Quite counterintuitively, in both cases the optimal states that have to be prepared in order to maximize the overall fidelity are not product states corresponding to M identical copies, but instead suitable M-partite entangled states: the simple protocol where one estimates the input state and re-prepares M identical copies of the estimated state is strictly suboptimal, even in the asymptotic limit.
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