# Comment on "Fully device-independent conference key agreement" [Phys. Rev. A 97, 022307 (2018)]

## TL;DR

This paper critically analyzes the DICKA protocol, demonstrating that its claimed honest implementation is impossible due to conflicting requirements, thus revealing fundamental limitations in device-independent conference key agreement.

## Contribution

It provides a rigorous critique of the DICKA protocol, showing the impossibility of its honest implementation in the tripartite setting using semidefinite programming.

## Key findings

- The honest implementation of DICKA fails due to conflicting measurement and Bell violation requirements.
- Semidefinite programming proves no suitable honest implementation exists in the tripartite case.
- The DICKA protocol is incomplete as a result of these fundamental limitations.

## Abstract

In this manuscript we discuss the device-independent conference key agreement (DICKA) protocol [Phys. Rev. A 97, 022307 (2018)]. We show that the suggested honest implementation fails, because perfect correlated measurement results and the required Bell-inequality violation cannot be achieved simultaneously, in contradiction to what is claimed. We further show via semidefinite programming that there cannot exist any suitable honest implementation in the tripartite setting, rendering the DICKA protocol incomplete.