Information-Calibrated Quantum Diffusion: Aligning Forward Noise with Reverse Recoverability

Abstract:Quantum diffusion models typically parameterize forward corruption by raw channel strength, even though equal parameter increments need not erase equal information or induce comparable inverse problems. We introduce the classical--quantum information decrement $\Delta_t=I(X{:}Q_{t-1})-I(X{:}Q_t)$ as an intrinsic diffusion coordinate for labeled quantum ensembles. Along depolarization, equalizing $\Delta_t$ yields the unique minimax discretization of the forward path, while universal recoverability gives the same quantity an operational reverse interpretation as an attainable expected log-fidelity budget for a label-independent CPTP recovery channel. Complementary continuity and pairwise-geometric converses lower-bound the optimal common-channel recovery error. We further show that local calibration is fundamentally insufficient for stochastic generation: even in a fixed noncommuting two-qubit system, identical local-fidelity laws and budget-feasible risks can coexist with macroscopically different output distributions. This motivates a stochastic learner combining theorem-scaled recovery constraints with distribution matching, for which we establish finite-sample calibration and compositional trace-Wasserstein control. On four-qubit TFIM, a controlled capacity extension reduces endpoint $\Wtr$ from $.622$ to $.424$ on all ten matched seeds and achieves lower $\Wtr$ than official QuDDPM ($.498$) with fewer trainable parameters.

arXiv:2608.14083 [quant-ph]

(or arXiv:2608.14083v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.14083 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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