Quantum enhancement of randomness distribution

TL;DR

This paper investigates the capacities of quantum channels to distribute shared randomness under various classical communication assistance scenarios, revealing cases where randomness distribution exceeds traditional communication capacities.

Contribution

It introduces the concept of randomness distribution capacities for quantum channels with classical assistance and compares them to communication capacities, highlighting new capacity relationships.

Findings

Mutual information bounds two-way assisted randomness capacity.

Capacities are equal for classical-quantum channels with assistance.

Back-assisted randomness capacity can surpass communication capacity.

Abstract

The capability of a given channel to communicate information is, a priori, distinct from its capability to distribute shared randomness. In this article we define randomness distribution capacities of quantum channels assisted by forward, back, or two-way classical communication and compare these to the corresponding communication capacities. With forward assistance or no assistance, we find that they are equal. We establish the mutual information of the channel as an upper bound on the two-way assisted randomness distribution capacity. This implies that all of the capacities are equal for classical-quantum channels. On the other hand, we show that the back-assisted randomness distribution capacity of a quantum-classical channels is equal to its mutual information. This is often strictly greater than the back-assisted communication capacity. We give an explicit example of such a separation where the randomness distribution protocol is noiseless.