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

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

URL: http://arxiv.org/abs/2402.15440v3
Date: Tue, 17 Sep 2024 18:39:57 GMT
Title: Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras
Authors: Cédric Arhancet,
Abstract summary: We investigate a new class of unital quantum computation channels on $mathrmM_2k$. We identify the matrix algebra $mathrmM_2k$ with a finite-dimensional fermion algebra. Our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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