Postselection-induced localization and coherence in quantum walks on heterogeneous networks

Abstract

Postselection of quantum trajectories is known to effectively introduce nonlinearity into dynamics of open quantum systems. We study the effect of such nonlinearity in continuous-time quantum walks (CTQWs) on networks with homogeneous and heterogeneous degree distributions. Using the recently proposed nonlinear Lindblad master equation (NLME), we investigate the dynamics under two decoherence mechanisms: Haken-Strobl decoherence and quantum stochastic walk (QSW). Our analysis reveals a striking dichotomy: under Haken-Strobl decoherence the nonlinear contributions precisely cancel, yielding a uniform steady state independent of postselection details under imperfect detection. In stark contrast, QSW decoherence permits postselection in this regime to break dynamical balance on heterogeneous networks, inducing robust localization preferentially at low-degree (peripheral) nodes. Remarkably, this localized state maintains finite quantum coherence. Extending our results to spin systems, we demonstrate that degree heterogeneity similarly stabilizes localization of spin-up excitations in spin-down backgrounds, enhancing pairwise entanglement preservation. These findings establish degree heterogeneity and postselection as joint control parameters for engineering quantum transport and localization in dissipative systems.