Flux control of measurement back-action and Leggett-Garg correlations in chiral quantum walks

Abstract

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 L\"uders 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 L\"uders 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 L\"uders bound. These results establish gauge-invariant flux as a resource for engineering local measurement back-action and temporal quantum correlations.