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

We investigate a new class of unital quantum channels on M2ᵏ, acting as radial multipliers when we identify the matrix algebra M2ᵏ 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 receiver when they share an unlimited amount of noiseless entanglement. Our approach relies on new connections between fermions algebras with the n-dimensional discrete hypercube \-1,1\ⁿ and more generally the Cantor group. 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.