Choi-level twirling of quantum channels: finite constructions and non-compact transformations
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| Format: | Preprint |
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2025
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| _version_ | 1866908851636273152 |
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| author | Markiewicz, Marcin Pawela, Łukasz Puchała, Zbigniew |
| author_facet | Markiewicz, Marcin Pawela, Łukasz Puchała, Zbigniew |
| contents | 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 $π^{\textrm{in}}(U)=U^{\otimes t_{\textrm{in}}}$ and $π^{\textrm{out}}(U)=U^{\otimes t_{\textrm{out}}}$, 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 $U^{\otimes(t_{\textrm{in}}+t_{\textrm{out}})}$, 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 $t=t_{\textrm{in}}+t_{\textrm{out}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Choi-level twirling of quantum channels: finite constructions and non-compact transformations Markiewicz, Marcin Pawela, Łukasz Puchała, Zbigniew Quantum Physics 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 $π^{\textrm{in}}(U)=U^{\otimes t_{\textrm{in}}}$ and $π^{\textrm{out}}(U)=U^{\otimes t_{\textrm{out}}}$, 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 $U^{\otimes(t_{\textrm{in}}+t_{\textrm{out}})}$, 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 $t=t_{\textrm{in}}+t_{\textrm{out}}$. |
| title | Choi-level twirling of quantum channels: finite constructions and non-compact transformations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.23586 |