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

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.

39 pages, final version