Capacities of Grassmann channels

Abstract

A new class of quantum channels called Grassmann channels is introduced and their classical and quantum capacity is calculated. The channel class appears in a study of the two-mode squeezing operator constructed from operators satisfying the fermionic algebra. We compare Grassmann channels with the channels induced by the bosonic two-mode squeezing operator. Among other results, we challenge the relevance of calculating entanglement measures to assess or compare the ability of bosonic and fermionic states to send quantum information to uniformly accelerated frames.Comment: 33 pages, Accepted in Journal of Mathematical Physics; The role of the (fermionic) braided tensor product for quantum Shannon theory, namely capacity formulas, elucidated; The conclusion on the equivalence of Unruh effect for bosons and fermions for quantum communication purposes made clear and even more precis