Postselection induced localization and coherence in quantum walks on heterogeneous networks

• URL: http://arxiv.org/abs/2603.17629v1
• Date: Wed, 18 Mar 2026 11:47:55 GMT
• Title: Postselection induced localization and coherence in quantum walks on heterogeneous networks
• Abstract summary: We study the effect of such non-linearity in continuous-time quantum walks (CTQWs) on networks with homogeneous and heterogeneous degree distributions.<n>Our analysis reveals a striking dichotomy: under Haken-Strobl decoherence the nonlinear contributions precisely cancel, yielding a uniform steady state independent of postselection details.<n>In stark contrast, QSW decoherence permits postselection to break dynamical balance on heterogeneous networks, inducing robust localization preferentially at low-degree nodes.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Postselection of quantum trajectories is known effectively introduce nonlinearity into dynamics of open quantum systems. We study the effect of such non-linearity 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 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. In stark contrast, QSW decoherence permits postselection 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 many-body spin systems, we demonstrate that degree heterogeneity similarly stabilizes localization of spin-up excitations in spin-down backgrounds, enhancing entanglement preservation. These findings establish degree heterogeneity and postselection as joint control parameters for engineering quantum transport and localization in dissipative dynamics.

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