Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras
Résumé
We investigate a new class of unital quantum channels on M_{2k}, acting as radial multipliers when we identify the matrix algebra M_{2k} 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.
Mots clés
- 94A40
- 46L07
- 81P45 noncommutative L p -spaces
- multipliers
- fermion algebras
- entropies
- quantum channels
- discrete hypercube
- quantum information theory
- 2020 Mathematics subject classification: 46L51
- 2020 Mathematics subject classification: 46L51 94A40 46L07 81P45 noncommutative L p -spaces multipliers fermion algebras entropies quantum channels discrete hypercube quantum information theory
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