Approximate pushforward designs and image bounds on approximations

Abstract:We extend the framework of quantum pushforward designs to the approximate setting, in which moment operators agree only up to finite precision. We first formulate a general transfer theorem for maps that act linearly at the level of moments. This separates direct applications, controlled by standard Schatten-norm estimates, from refinements that use additional tensorial structure. Dephasing is shown to be contractive and therefore sends an approximate projective design to a simplex design without increasing its error. Ordinary partial-trace estimates give immediate bounds for mixed-state and channel designs. We then prove a sharp Schatten-norm bound for the partial trace restricted to the totally symmetric subspace. This replaces the full-environment norm coefficient by one governed by a symmetric-subspace dimension and yields asymptotically tighter estimates for both mixed-state and channel designs. Numerical simulations for induced mixed-state designs are consistent with the resulting hierarchy of bounds.

26 pages, 2 figures, comments welcome!

arXiv:2512.01858 [quant-ph]

(or arXiv:2512.01858v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.01858 Focus to learn more arXiv-issued DOI via DataCite

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