Arbitrarily Small Amounts of Correlation for Arbitrarily Varying Quantum Channels

TL;DR

This paper demonstrates that minimal correlation resources suffice for reliable quantum communication over arbitrarily varying channels, challenging the necessity of perfect shared randomness and simplifying channel conditions.

Contribution

It shows that limited correlated resources enable capacity achievement without perfect shared randomness, and introduces simplified conditions for channel symmetrizability.

Findings

Limited correlation resources are sufficient for capacity achievement.

Shared randomness is a costly resource and not always necessary.

A simplified symmetrizability condition for quantum channels is established.

Abstract

As our main result we 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 simplifed symmetrizability condition for finite arbitrarily varying quantum channels.