发表机构
Joint Quantum Institute, NIST/University of Maryland; Joint Center for Quantum Information and Computer Science, NIST/University of Maryland; Centre for Quantum Technologies (CQT), National University of Singapore; Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR); Center for Quantum Software and Innovation, University of Technology Sydney; IonQ, Inc.; Volgenau Department of Physics, United States Naval Academy（联合量子研究所，美国国家标准与技术研究院/马里兰大学; 量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学; 量子技术中心，新加坡国立大学; 量子创新中心，科学技术研究局; 量子软件与创新中心，悉尼科技大学; IonQ公司; 沃尔格瑙物理系，美国海军学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明在离散相位随机化下，压缩真空态相比相干态在相位估计中具有超指数优势，并给出具体协议与噪声鲁棒性分析。
AI 中文摘要
量子计量学中的一个典型任务是相位估计。对于该任务，通常认为在关于先验信息的合理假设下，灵敏度上的二次优势是使用量子资源所能提供的最大可能优势。在这项工作中，我们考虑一个信道，它除了实现一个小的未知目标相位偏移外，还实现一个角度为 $2\pi k/M$ 的相位偏移，其中 $k$ 是一个均匀随机的未知整数。我们证明，在每次信道使用的平均光子数受约束的条件下，使用压缩真空态所能达到的量子费希尔信息（QFI）与使用相干态所能达到的QFI之间存在超指数分离。这一优势适用于任何通过相位协变信道从相干态获得的态。具体而言，当每次信道使用的平均光子数为1时，它们的QFI之比随 $\Omega[(M/\sqrt{2}e)^M]$ 增长。对于每次信道使用的平均光子数为 $M/\log(M)$ 的情况，压缩真空态的QFI为 $\Omega(M^{3/2}/\sqrt{\log(M)})$，而相干态的QFI至多为 $\exp[-M\log\log(M)+O(M)]$。我们用非渐近估计结果补充了这一QFI分析。对于每次信道使用的平均光子数为 $M/\log M$ 的情况，一个显式的压缩真空协议使用 $O(\sqrt{M\log M})$ 次信道使用即可将相位估计精度达到 $O(1/M)$，而每个相干态协议至少需要 $\exp[M\log\log M-O(M)]$ 次信道使用。我们考虑了噪声的影响，并表明它们的QFI之比仍可随 $M$ 超指数增长。最后，在固定的光学损耗和热噪声下，选择 $\bar n=M^2/(\log M)^{3/2}$ 允许使用零差检测的压缩真空态以亚多项式次信道使用达到 $O(1/M)$ 的精度，而指定经典族中的每个协议都需要超多项式次信道使用。
英文摘要
A paradigmatic task in quantum metrology is that of phase estimation. For this task it is commonly believed, under reasonable assumptions about prior information, that a quadratic advantage in sensitivity is the maximum possible advantage offered by the use of quantum resources. In this work, we consider a channel that implements a phase shift by an angle $2πk/M$, where $k$ is a uniformly random unknown integer, in addition to a small unknown phase shift of interest. We show that, subject to a constraint on the mean photon number per channel use, there is a super-exponential separation between the quantum Fisher information (QFI) attainable using a squeezed vacuum state and that attainable using coherent states. This advantage holds over any state obtained from a coherent state via phase covariant channels. Specifically, when the mean photon number per channel use is 1, the ratio of their QFI grows as $Ω[(M/\sqrt{2}e)^M]$. For a mean photon number per channel use of $M/\log(M)$, the squeezed vacuum QFI is $Ω(M^{3/2}/\sqrt{\log(M)})$, whereas for a coherent state it is at most $\exp[-M\log\log(M)+O(M)]$. We complement this QFI analysis with non-asymptotic estimation results. For a mean photon number per channel use of $M/\log M$, an explicit squeezed-vacuum protocol estimates the phase to accuracy $O(1/M)$ using $O(\sqrt{M\log M})$ channel uses, whereas every coherent state protocol requires at least $\exp[M\log\log M-O(M)]$ channel uses. We consider the effects of noise and show that the ratio of their QFIs can still grow super-exponentially in $M$. Finally, under fixed optical loss and thermal noise, choosing $\bar n=M^2/(\log M)^{3/2}$ allows squeezed vacuum with heterodyne detection to achieve accuracy $O(1/M)$ using sub-polynomially many channel uses, whereas every protocol in the specified classical family requires super-polynomially many.
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