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- W4313679891 abstract "Previous noncommutative Bohnenblust--Hille inequalities addressed operator decompositions in the tensor product space $SU(2)^{otimes n}$ cite{HCP22,VZ22}. Here we prove the inequalities for product spaces of arbitrary local dimension, e.g., $SU(N)^{otimes n}$ or $n$-fold tensor products of $Ntimes N$ Hermitian matrices. We treat operator decompositions in both the Gell-Mann and Heisenberg-Weyl bases by reducing to commutative cases. The latter basis is reduced to a scalar Bohnenblust-Hille inequality for cyclic groups which we also prove. Applications to quantum junta theorems and learning qudit quantum observables in the Probably Approximately Correct framework are also listed." @default.
- W4313679891 created "2023-01-08" @default.
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- W4313679891 date "2023-01-03" @default.
- W4313679891 modified "2023-09-25" @default.
- W4313679891 title "Noncommutative Bohnenblust-Hille inequality in the Heisenberg-Weyl and Gell-Mann bases with applications to fast learning" @default.
- W4313679891 doi "https://doi.org/10.48550/arxiv.2301.01438" @default.
- W4313679891 hasPublicationYear "2023" @default.
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