发表机构
The University of Hong Kong（香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在有限维量子计量中，不确定因果序相对确定序可实现无界能量优势，通过建立离散高斯波包的近似Weyl关系，在有限样本下实现任意大的分离。
AI 中文摘要
已知不确定因果序在量子计量中能提供增强，尤其在对谐振子几何相位的测量中展现出无界优势。然而，这一优势特定于无限维设定，其有限维类比仍然难以捉摸，近期发现表明有限维中的优势可能从根本上受限于有界常数因子。在此，我们证明在有限样本范围内，有限维系统实际上能产生任意大的优势。具体而言，我们在估计与离散位置和动量算符在d维量子系统上生成的N组位移相关的几何相位时，建立了确定与不确定因果序之间的无界分离：对于任意给定常数R，存在N和d=Ω(N^2)的值，使得当测量次数ν满足ν=O(exp(πd/16)/poly(d))时，具有不确定序的策略使用的初始探针能量比所有达到相同均方误差的确定序策略所需探针能量低R倍。换言之，不确定序提供的能量节省随问题参数任意增大。为证明此结果，我们建立了离散高斯波包近似Weyl关系，该关系具有独立的技术意义。
英文摘要
Indefinite causal order is known to offer enhancements in quantum metrology, notably including an unbounded advantage in the measurement of a geometric phase of a harmonic oscillator. This advantage, however, is specific to the infinite dimensional setting, and its finite dimensional analogue remains elusive, with recent findings suggesting that advantages in finite dimensions may be fundamentally limited to bounded constant factors. Here we show that, in fact, arbitrarily large advantages arise for finite dimensional systems in the finite sample regime. Specifically, we establish an unbounded separation between definite and indefinite causal order in the estimation of a geometric phase associated to two sets of $N$ displacements generated by discrete position and momentum operators on a $d$-dimensional quantum system: for any given constant $R$, there exist values of $N$ and $d=Ω(N^2)$ such that a strategy with indefinite order uses an initial probe with $R$ times less energy than the probe required by every strategy with definite order achieving the same mean squared error, whenever the number of measurement shots $ν$ is bounded as $ν=\mathcal{O}(\exp(πd/16)/\mathrm{poly}(d))$. In other words, indefinite order offers an energy saving that grows arbitrarily large with the parameters of the problem. To prove this result, we establish an approximate Weyl relation for discrete Gaussian wavepackets, which is of independent technical interest.
Comments47 pages, 3 figures
