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Article overview
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Noncommutative Bohnenblust-Hille inequality in the Heisenberg-Weyl and Gell-Mann bases with applications to fast learning | | Joseph Slote
; Alexander Volberg
; Haonan Zhang
; | | Date: |
4 Jan 2023 | | 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 $N imes N$ 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. | | Source: | arXiv, 2301.01438 | | Services: | Forum | Review | PDF | Favorites | |
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