Channel-Constrained Information Scheduling for Quantum Diffusion

Abstract

Information-based diffusion schedules organize the reverse problem by prescribing how much source information remains after each forward step. For mixed-state quantum diffusion, density-level targets need not correspond to trajectories reachable from the current realization. We introduce \emph{channel-constrained information scheduling}: each step optimizes over source-blind pure-state refinements reachable from the current state-resolved record through the prescribed channel. This defines a channel-constrained information clock $V_ξ$, whose inverse selects the least-corrupting step that reaches a target information level. Recursive inversion constructs a realizable equal-information schedule minimizing the worst source-information burden in Bayes reverse prediction. We establish attainment, continuity, monotonicity, convexity, finite support, and exact primal/dual formulations for $V_ξ$. We further give a sharp structural characterization: binary-qubit depolarizing trajectories attain the density-level Belavkin--Staszewski envelope, whereas every $d\ge3$ admits binary noncommuting families with a strict static--dynamic separation. Qutrit experiments show that the proposed scheduler nearly equalizes the realized multi-step burden, and learned reverse predictors recover the predicted allocation.