Noncommutative Bohnenblust--Hille Inequality for qudit systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909223013580800 |
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| author | Slote, Joseph Volberg, Alexander Zhang, Haonan |
| author_facet | Slote, Joseph Volberg, Alexander Zhang, Haonan |
| contents | Previous noncommutative Bohnenblust--Hille (BH) inequalities addressed operator decompositions in the tensor-product space $M_2(\mathbb{C})^{\otimes n}$; \emph{i.e.,} for systems of qubits \cite{HCP22,VZ23}. Here we prove noncommutative BH inequalities for operators decomposed in tensor-product spaces of arbitrary local dimension, \emph{i.e.,} $M_K(\mathbb{C})^{\otimes n}$ for any $K\geq2$ or on systems of $K$-level qudits. We treat operator decompositions in both the Gell-Mann and Heisenberg--Weyl basis, reducing to the recently-proved commutative hypercube BH \cite{DMP} and cyclic group BH \cite{SVZ} inequalities respectively. As an application we discuss learning qudit quantum observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncommutative Bohnenblust--Hille Inequality for qudit systems Slote, Joseph Volberg, Alexander Zhang, Haonan Functional Analysis Mathematical Physics Previous noncommutative Bohnenblust--Hille (BH) inequalities addressed operator decompositions in the tensor-product space $M_2(\mathbb{C})^{\otimes n}$; \emph{i.e.,} for systems of qubits \cite{HCP22,VZ23}. Here we prove noncommutative BH inequalities for operators decomposed in tensor-product spaces of arbitrary local dimension, \emph{i.e.,} $M_K(\mathbb{C})^{\otimes n}$ for any $K\geq2$ or on systems of $K$-level qudits. We treat operator decompositions in both the Gell-Mann and Heisenberg--Weyl basis, reducing to the recently-proved commutative hypercube BH \cite{DMP} and cyclic group BH \cite{SVZ} inequalities respectively. As an application we discuss learning qudit quantum observables. |
| title | Noncommutative Bohnenblust--Hille Inequality for qudit systems |
| topic | Functional Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2406.08509 |