量子噪声中时空相关性的量化与界定

中文摘要 AI 辅助

量子噪声中的空间和时间相关性对量子信息处理中常用的局域马尔可夫模型提出了挑战。我们开发了一个统一的操作性框架，用于量化一般量子过程中的时间、空间以及总时空相关性。利用过程张量，我们通过相对于马尔可夫过程、空间局域过程以及完全无关联过程的最优可区分性来定义这些量。对可容许探测梳的优化确保了在每一个保持相应自由集的超过程下的单调性，而Choi态泛函和受限探测则提供了可达到的下界。我们在相关性度量之间建立了层级关系和插值关系，并推导了量子存储器传输的时间相关性的维度依赖上界，其中经典存储器具有更紧的上界，同时系统维度也施加了普适上限。这些界限将经过认证的下界估计转化为最小存储器维度的见证、存储器维度约束下的非经典性见证以及假定过程模型不一致性的见证。我们通过具有ZZ和XY相互作用的有效超导量子比特模型展示了结果，这些模型表现出经典存储器、量子存储器和系统维度上限的饱和。这些结果为表征和解决量子器件中时空相关误差的实际方法铺平了道路。

英文摘要

Spatial and temporal correlations in quantum noise challenge the local Markovian models commonly used in quantum information processing. We develop a unified operational framework for quantifying temporal, spatial, and total spatiotemporal correlations in general quantum processes. Using process tensors, we define these quantities through optimal distinguishability from Markovian, spatially local, and fully uncorrelated processes. Optimization over admissible probing combs ensures monotonicity under every superprocess that preserves the corresponding free set, while Choi-state functionals and restricted probes provide accessible lower bounds. We establish hierarchy and interpolation relations among the correlation measures and derive dimension-dependent upper bounds on temporal correlations transmitted by quantum memories, with tighter bounds for classical memory, together with universal ceilings imposed by the system dimension. These bounds turn certified lower estimates into witnesses of minimum memory dimension, nonclassicality under a memory-dimension constraint, and inconsistencies in the assumed process model. We illustrate the results with effective superconducting-qubit models featuring \(ZZ\) and \(XY\) interactions, exhibiting saturation of classical-memory, quantum-memory, and system-dimension ceilings. These results pave the way toward practical approaches to characterizing and addressing spatiotemporally correlated errors in quantum devices.

发表机构

• Sao Carlos Institute of Physics, University of Sao Paulo（圣卡洛斯物理研究所，圣保罗大学）

机构由 AI 辅助整理，请以论文原文为准。