Message transmission over classical quantum channels with a Jammer with side information; correlation as resource and common randomness generating
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In this paper we analyze the capacity of a general model for arbitrarily varying classical-quantum channels when the sender and the receiver use a weak resource. In this model a jammer has side information about the channel input. We determine the correlation assisted capacity of AVCQCs with a jammer knowing the channel input. We deliver a single letter formula for the correlation assisted capacity. This formula as a function of the channel parameters is Turing computable. The single letter characterization is surprising, on the one hand because correlation is the weakest resource in the hierarchy of resources, on the other hand because the deterministic capacity formula for arbitrarily varying channels with informed jammer is still an open problem, even for classical arbitrarily varying channels, where the well-know Shannon's zero-error capacity is contained as a special case of this scenario. As an application,we determine the correlation assisted common randomness capacity. We also analyze these both capacities when only a small amount of correlation is available. For the correlation assisted common randomness capacity we show a further interesting aspect: For a sufficient amount of "public communication", common randomness capacity is Turing computable, however without this public communication's constrain, the correlation assisted common randomnesscapacity is in general not Banach-Mazur computable and thus not Turing computable.
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