# Message Transmission over Classical Quantum Channels with a Jammer with Side Information: Correlation as Resource, Common Randomness Generation

## TL;DR

This paper investigates the capacity of arbitrarily varying classical-quantum channels with a jammer having side information, establishing a single-letter formula for correlation-assisted capacity and exploring its implications for common randomness generation.

## Contribution

It derives a single-letter formula for correlation-assisted capacity in AVCQCs with an informed jammer and analyzes the computability of the associated capacities.

## Key findings

- Derived a single-letter formula for correlation-assisted capacity.
- Showed that common randomness generation capacity can be non-Turing computable without public communication.
- Established that capacity evaluation can be impossible algorithmically even without known deterministic capacity formulas.

## Abstract

In this paper we analyze the capacity of a general model for arbitrarily varying classical-quantum channels (AVCQCs) when the sender and the receiver use correlation as a resource. In this general model, a jammer has side information about the channel input. We determine a single letter formula for the correlation assisted capacity. As an application of our main result, we determine the correlation assisted common randomness generation capacity. In this scenario the two channel users have access to correlation as a resource,and further use an AVCQC with an informed jammer for additional discussion. The goal is to create common randomness between the two channel users. We also analyze these capacity formulas when only a small number of signals from the correlation are available. For the correlation assisted common randomness generation capacity, we show an additional interesting property: For a sufficient amount of "public communication", common randomness generation capacity is Turing computable, however without this public communication constraint, the correlation assisted common randomness generation capacity is, in general, not Turing computable. Furthermore, we show that even without knowing the capacity formula of the deterministic capacity using maximal error criterion, we can show that it is impossible to evaluate the performance algorithmically on any current or future digital computer.