未知因果结构信号的量子计量学
Quantum Metrology for Signals with an Unknown Causal Structure
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中文总结 AI 辅助
本文针对信号因果结构未知的量子传感，证明测量方案必须采用干涉测量，给出Fisher信息界限并推导时空海森堡极限，揭示N^2标度源于跨时空共享参考系的相干性。
中文摘要 AI 辅助
量子传感协议通常预设每个信号作用的位置和时间，然而在散射和雷达等实验中，这些信息事先无法获得。我们证明，即使只允许离散相互作用，因果不可知性也会迫使测量方案采用干涉测量。利用最近发展的时空量子态形式描述传感事件，我们证明了干涉仪的Fisher信息受局域生成元范数平方和的约束，与事件如何排序无关。当物理膨胀在扩大后的事件集合上具有时空态时，非幺正和时空相关信号同样可以得到解释。值得注意的是，只要目标和辅助事件的完整集合具有时空态，该界限的成立无需预设一个对事件进行排序的背景时空。我们证明该界限产生时空海森堡极限，并通过信号“修饰”的时空态的边际来刻画其饱和。Fisher信息随N个传感事件呈N^2标度，源于单个参考系统跨时空共享的相干性，而独立重复的干涉测量则遵循标准量子极限。
英文摘要
Quantum sensing protocols usually presuppose where and when each signal acts, yet this information is unavailable beforehand in experiments such as scattering and radar. We show that causal agnosticity forces a measurement scheme to be interferometric even when only discrete interactions are allowed. Describing the sensing events in the recently developed quantum state over spacetime formalism, we then prove that the Fisher information of an interferometer is bounded by the squared sum of the local generator norms, independently of how the events are ordered. Nonunitary and spatiotemporally correlated signals can be explained as well when their physical dilation has a spacetime state on the enlarged events. Notably, the bound holds without presupposing a background spacetime that orders the events whenever the full collection of target and auxiliary events has a spacetime state. We show that this bound yields the spacetime Heisenberg limit and characterize its saturation through marginals of the spacetime state `dressed' by the signal. The $N^2$ scaling of the Fisher information with $N$ sensing events arises from the coherence of a single reference system shared across spacetime, whereas independently repeated interferometry obeys the standard quantum limit.
发表机构
- Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）
- Sejong University（世宗大学）
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