Capacity of Quantum Arbitrarily Varying Channels

We prove that the average error capacity Cq of a quantum arbitrarily varying channel (QAVC) equals 0 or else the random code capacity ¯ C (Ahlswede’s dichotomy). We also establish a necessary and sufficient condition for Cq> 0. I. Introduction and Results We define the QAVC by the double indexed finite set of density operators ρx,s, x ∈ X, s ∈ S on Cd. X is the set of code symbols and S is the set of states of the QAVC. As usual we consider the scheme of n uses of the channel. A code C of cardinality N and length n is a set of pairs {(cn i,Ii), i = 1,...N}, wher