Classification and implementation of unitary-equivariant and permutation-invariant quantum channels

• URL: http://arxiv.org/abs/2510.08154v1
• Date: Thu, 09 Oct 2025 12:35:39 GMT
• Title: Classification and implementation of unitary-equivariant and permutation-invariant quantum channels
• Authors: Laura Mančinska, Elias Theil,
• Abstract summary: Many quantum information tasks use inputs of the form $rhootimes m$, which naturally induce permutation and unitary symmetries.<n>We classify all quantum channels that respect both symmetries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many quantum information tasks use inputs of the form $\rho^{\otimes m}$, 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.

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