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arXiv · 2402.15440

Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras

Cédric Arhancet
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Abstract

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.

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Cédric Arhancet. 2024-02-23. Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras. https://arxiv.org/abs/2402.15440

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