论文标题
相干有限的相位估计
Phase estimation with limited coherence
论文作者
论文摘要
我们研究了探测器的相干性$ c $的量子相估计的最终精度限制。对于纯状态，我们给出可达到的最小估计差异，$ v（c）$，而当探头系统大小为$ n $的尺寸很大时，最佳状态在渐近限制下。我们证明，只有$ c $ scale作为$ n $具有足够大比例的因素，纯状态才是最佳状态，而最佳状态的排名随着$ c $的降低而增加，最终成为全级别。我们表明，该方差表现出像海森堡一样的缩放，$ v（c）\ sim a_n/c^2 $，其中$ a_n $降低至$π^2/3 $，$ n $增加，导致与维度独立的关系。
We investigate the ultimate precision limits for quantum phase estimation in terms of the coherence, $C$, of the probe. For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the asymptotic limit when the probe system size, $n$, is large. We prove that pure states are optimal only if $C$ scales as $n$ with a sufficiently large proportionality factor, and that the rank of the optimal state increases with decreasing $C$, eventually becoming full-rank. We show that the variance exhibits a Heisenberg-like scaling, $V(C) \sim a_n/C^2$, where $a_n$ decreases to $π^2/3$ as $n$ increases, leading to a dimension-independent relation.
