发表机构
School of Physics, Sun Yat-sen University; Hefei National Laboratory, University of Science and Technology of China（中山大学物理学院; 中国科学技术大学合肥国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明不定因果序（ICO）无法为量子信道估计带来渐近计量优势，其最优性能与并行策略相当，明确了不定因果性的计量资源作用。
AI 中文摘要
具有不定因果序（ICO）的量子计量学因有望突破传统固定序策略的局限而受到广泛关注，一个关键的开放问题是ICO能否从根本上提升渐近精度标度。在本研究中，我们针对有限维量子信道的单个参数估计问题，该参数编码在N次相同的有限维量子信道使用中，填补了这一研究空白。我们首先为全通用ICO过程矩阵类别建立了通用的海森堡标度上界，并证明对于幺正信道，其最优量子费舍尔信息（QFI）与并行策略的QFI完全一致。对于有噪信道，一个结构优化的界表明，在并行策略下受限于标准量子极限（SQL）的信道，在通用ICO策略下仍受限于SQL。最重要的是，我们推导了一个渐近紧致（AT）界，通过证明通用ICO策略与最优并行策略在SQL和海森堡两个区域的QFI主导系数完全相同，从而排除了ICO存在渐近优势的剩余可能性。对于具有因果序量子控制的量子电路这一受操作驱动的类别，我们进一步得到了有限次查询精度的迭代约束，其渐近极限与AT界一致。我们的研究结果明确了不定因果性作为量子信道计量资源的最终作用。
英文摘要
Quantum metrology with indefinite causal order (ICO) has attracted intense interest due to its potential to surpass the limitations of conventional fixed-order strategies. A key open question is whether ICO can fundamentally enhance asymptotic precision scaling. In this work, we bridge this gap for the estimation of a single parameter encoded in $N$ identical uses of a finite-dimensional quantum channel. We first establish a universal Heisenberg-scaling upper bound for the full general ICO process-matrix class and show that for unitary channels its optimal quantum Fisher information (QFI) coincides exactly with that of parallel strategies. For noisy channels, a structurally refined bound shows that channels restricted to the standard quantum limit (SQL) under parallel strategies remain SQL-limited under general ICO strategies. Most significantly, an asymptotically tight (AT) bound is derived to close the remaining possibility of an asymptotic ICO advantage by showing that general ICO and optimal parallel strategies have exactly the same leading QFI coefficient in both the SQL and Heisenberg regimes. For the operationally motivated class of quantum circuits with quantum control of causal order, we further obtain an iterative constraint on finite-query precision whose asymptotic limit agrees with that of the AT bound. Our results clarify the ultimate role of indefinite causality as a metrological resource for quantum channel estimation.
Comments7 pages, 2 figures; Supplemental Material included (23 pages, 2 figures)
