Arbitrarily small amounts of correlation for arbitrarily varying quantum channels

Abstract

As our main result show that in order to achieve the randomness assisted message and entanglement transmission capacities of a finite arbitrarily varying quantum channel it is not necessary that sender and receiver share (asymptotically perfect) common randomness. Rather, it is sufficient that they each have access to an unlimited amount of uses of one part of a correlated bipartite source. This access might be restricted to an arbitrary small (nonzero) fraction per channel use, without changing the main result. We investigate the notion of common randomness. It turns out that this is a very costly resource -generically, it cannot be obtained just by local processing of a bipartite source. This result underlines the importance of our main result. Also, the asymptotic equivalence of the maximal-and average error criterion for classical message transmission over finite arbitrarily varying quantum channels is proven. At last, we prove a simplified symmetrizability condition for finite arbitrarily varying quantum channels. C 2013 AIP Publishing LLC. [http://dx.

On the weakest resource for coordination in AV-MACs with conferencing encoders

“…Proof: As noted in [2] (details in [4]) we may assume that |U ν | = 2, otherwise the senders can apply binary functions b 1 , b 2 such that (b 1 (U 1 ), (b 2 (U 2 )) and V are still stochastically dependent. Let ε, λ > 0.…”