Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913605109153792 |
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| author | Arhancet, Cédric |
| author_facet | Arhancet, Cédric |
| contents | We investigate a new class of unital quantum channels on $\mathrm{M}_{2^k}$, acting as radial multipliers when we identify the matrix algebra $\mathrm{M}_{2^k}$ with a finite-dimensional fermion algebra. Our primary contribution lies in the precise computation of the (optimal) rate at which classical information can be transmitted through these channels from a sender to a receiver when they share an unlimited amount of entanglement. Our approach relies on new connections between fermion algebras with the $n$-dimensional discrete hypercube $\{-1,1\}^n$. Significantly, our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup. This advancement not only provides deeper insights into the structure and behaviour of these channels but also enhances our understanding of Quantum Information Theory in a dimension-independent context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras Arhancet, Cédric Quantum Physics Mathematical Physics Functional Analysis Operator Algebras We investigate a new class of unital quantum channels on $\mathrm{M}_{2^k}$, acting as radial multipliers when we identify the matrix algebra $\mathrm{M}_{2^k}$ with a finite-dimensional fermion algebra. Our primary contribution lies in the precise computation of the (optimal) rate at which classical information can be transmitted through these channels from a sender to a receiver when they share an unlimited amount of entanglement. Our approach relies on new connections between fermion algebras with the $n$-dimensional discrete hypercube $\{-1,1\}^n$. Significantly, our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup. This advancement not only provides deeper insights into the structure and behaviour of these channels but also enhances our understanding of Quantum Information Theory in a dimension-independent context. |
| title | Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras |
| topic | Quantum Physics Mathematical Physics Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2402.15440 |