02013nas a2200157 4500000000100000008004100001260001500042100002200057700001900079700002200098245009800120856003700218300000700255520155200262022004101814 2026 d c25/02/20261 aMarcin Markiewicz1 aŁukasz Pawela1 aZbigniew Puchała00aChoi-level twirling of quantum channels: finite constructions and non-compact transformations uhttps://arxiv.org/abs/2512.23586 a153 a

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–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 in(U) = U ⊗tin and π out(U) = U ⊗tout , we introduce a partial-transpose reduction that removes the contragredient action and converts the mixed (walled Brauer) channel twirl into an ordinary Schur–Weyl twirl of the partially transposed Choi operator under U ⊗(tin+tout) , 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 “dual” 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 = tin + tout.

 a1751-8121 (online), 1751-8113 (druk)