Classification and implementation of unitary-equivariant and permutation-invariant quantum channels
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914083698114560 |
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| author | Mančinska, Laura Theil, Elias |
| author_facet | Mančinska, Laura Theil, Elias |
| contents | Many quantum information tasks use inputs of the form $ρ^{\otimes m}$, which naturally induce permutation and unitary symmetries. We classify all quantum channels that respect both symmetries - i.e. unitary-equivariant and permutation-invariant quantum channels from $(\mathbb{C}^{d})^{\otimes m}$ to $(\mathbb{C}^{d})^{\otimes n}$ - via their extremal points. Operationally, each extremal quantum channel factors as unitary Schur sampling $\rightarrow$ an irrep-level unitary-equivariant quantum channel $\rightarrow$ the adjoint unitary Schur sampling. We give a streaming implementation ansatz that uses an efficient streaming implementation of unitary Schur sampling together with a resource-state primitive, and we apply it to state symmetrization, symmetric cloning, and purity amplification. In these applications we obtain polynomial-time algorithms with exponential memory improvements in $m,n$. Further, for symmetric cloning we present, to our knowledge, the first efficient (polynomial-time) algorithm with explicit memory and gate bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification and implementation of unitary-equivariant and permutation-invariant quantum channels Mančinska, Laura Theil, Elias Quantum Physics Many quantum information tasks use inputs of the form $ρ^{\otimes m}$, which naturally induce permutation and unitary symmetries. We classify all quantum channels that respect both symmetries - i.e. unitary-equivariant and permutation-invariant quantum channels from $(\mathbb{C}^{d})^{\otimes m}$ to $(\mathbb{C}^{d})^{\otimes n}$ - via their extremal points. Operationally, each extremal quantum channel factors as unitary Schur sampling $\rightarrow$ an irrep-level unitary-equivariant quantum channel $\rightarrow$ the adjoint unitary Schur sampling. We give a streaming implementation ansatz that uses an efficient streaming implementation of unitary Schur sampling together with a resource-state primitive, and we apply it to state symmetrization, symmetric cloning, and purity amplification. In these applications we obtain polynomial-time algorithms with exponential memory improvements in $m,n$. Further, for symmetric cloning we present, to our knowledge, the first efficient (polynomial-time) algorithm with explicit memory and gate bounds. |
| title | Classification and implementation of unitary-equivariant and permutation-invariant quantum channels |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.08154 |