Choi-level twirling of quantum channels: finite constructions and non-compact transformations
Year: 2026
Type: article
Abstract: 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 ⊗ t in and π out ( U ) = U ⊗ t out , we adapt a partial-transpose correspondence to the Choi representation of channels. This converts the mixed channel twirl under U ⊗ t out ⊗ U ― ⊗ t in into an ordinary Schur–Weyl twirl of the partially transposed Choi operator under U ⊗ ( t in + t out ) , enabling explicit permutation-based formulas without constructing walled Brauer idempotents or mixed Schur transforms. Beyond compact symmetries, we formulate a Choi-level Cartan averaging procedure for reductive, generally non-unitary transformations 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 sector-wise implementation using unitary 1 -design maps on invariant sectors, and a design-like reconstruction showing that finite weighted sets reproducing the relevant t -th moment exactly reconstruct the averaged Choi operator for t = t in + t out .
Authors: Marcin Markiewicz, Łukasz Pawela, Zbigniew Puchała
Institutions: University of Gdańsk, Polish Academy of Sciences
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Narodowe Centrum Nauki
Award: G7061601885
OpenAlex ID: W7196959098