AI 中文总结
该研究提出规范不变通量可调控手性量子行走的测量反作用与Leggett-Garg关联，确定了饱和Lüders界的机制，为量子关联调控提供了通量工程资源。
AI 中文摘要
规范不变通量调控手性连续时间量子行走中的干涉。我们研究其如何影响单个顶点处的序列测量，采用二分可观测量区分返回该顶点与占据其补集。对于初始定域于被测顶点的行走者，完整的两时间统计（包括测量反作用与Leggett-Garg关联子）由返回振幅精确确定，将时间关联与局部谱测度、规范不变闭行走干涉关联起来。短时间内，主导扰动独立于Peierls相位，而通量敏感性通过闭行走间的干涉在更高阶出现。我们进一步确定了饱和Lüders界的图无关充分机制：通量可将根动力学简化为具有相等谱权重的平衡二维Krylov子空间，得到有限时间下达到3/2的Lüders界的建设性通量工程准则。该机制在双通量菱形图上精确实现，其中相消干涉使额外根模式为暗模式，局部反作用依赖于两个独立通量的相对组合。对于通量穿线环，精确的绕数展开揭示了奇偶依赖的 onset：偶环的主导通量对比通常出现在t^N阶，奇环则出现在t^{2N}阶。在所考察的环中，通量可增强Leggett-Garg的最大违反或将强违反移至更早的测量时间，半通量驱动四站点环达到Lüders界。这些结果确立了规范不变通量作为调控局部测量反作用与时间量子关联的资源。
英文摘要
Gauge-invariant fluxes control interference in chiral continuous-time quantum walks. We investigate how they affect sequential measurements at a single vertex, using a dichotomic observable that distinguishes return to that vertex from occupation of its complement. For a walker initially localized at the measured vertex, the complete two-time statistics, including measurement back-action and Leggett--Garg correlators, are determined exactly by the return amplitude, connecting temporal correlations to the local spectral measure and gauge-invariant closed-walk interference. At short times, the leading disturbance is independent of the Peierls phases, whereas flux sensitivity enters at higher orders through interference among closed walks. We further identify a graph-independent sufficient mechanism for saturating the Lüders bound: flux can reduce the rooted dynamics to a balanced two-dimensional Krylov subspace with equal spectral weights, yielding a constructive flux-engineering criterion for attaining the Lüders bound of $3/2$ at finite times. The mechanism is realized exactly on a two-flux diamond graph, where destructive interference renders additional rooted modes dark and the local back-action depends on relative combinations of the two independent fluxes. For flux-threaded cycles, an exact winding-number expansion reveals a parity-dependent onset: the leading flux contrast occurs generically at order $t^N$ for even cycles and $t^{2N}$ for odd cycles. Across the cycles examined, flux can either enhance the maximal Leggett--Garg violation or shift strong violations to earlier measurement times, with half flux driving the four-site cycle to the Lüders bound. These results establish gauge-invariant flux as a resource for engineering local measurement back-action and temporal quantum correlations.
Comments17 pages, 4 figures. Comments are welcome
