@article{bibcite_16184,
  author = {Marcin Markiewicz and {\L}ukasz Pawela and Zbigniew Pucha{\l}a},
  title = {Choi-level twirling of quantum channels: finite constructions and non-compact transformations},
  abstract = {<p>Twirling, i.e. averaging over symmetry actions, is a standard tool for reducing quantum states and channels to a symmetry-invariant form. We study channel twirling from the perspective of the channel{\textendash}state duality and provide a constructive Choi-level description of the averaging map induced by arbitrary input/output representations. Our main technical result concerns the collective setting: for π <sup>in</sup>(U) = U <sup>(x)t</sup><sub><sup>in</sup></sub> and π <sup>out</sup>(U) = U <sup>(x)t</sup><sub><sup>out</sup></sub> , we introduce a partial-transpose reduction that removes the contragredient action and converts the mixed (walled Brauer) channel twirl into an ordinary Schur{\textendash}Weyl twirl of the partially transposed Choi operator under U <sup>(x)(t</sup><sub><sup>in</sup></sub><sup>+t</sup><sub><sup>out</sup></sub><sup>)</sup> , enabling explicit permutation-based formulas without constructing walled Brauer idempotents or mixed Schur transforms. Beyond compact symmetries, we extend channel twirling to reductive, generally non-unitary groups via Cartan decomposition and obtain an invariant-sector decomposition of the averaged Choi operator with weights determined solely by the Abelian Cartan component. Finally, we provide two finite realizations of channel averaging: a {\textquotedblleft}dual{\textquotedblright} implementation as a convex mixture of unitary-1-design channels acting on invariant sectors, and a design-like reconstruction showing that weighted group t-designs induce channel t-designs for t = t<sub>in</sub> + t<sub>out</sub>.</p>},
  year = {2026},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  pages = {15},
  month = {25/02/2026},
  issn = {1751-8121 (online), 1751-8113 (druk)},
  url = {https://arxiv.org/abs/2512.23586},
  doi = {10.1088/1751-8121/ae965b},
}