Fundamental limitations on the device-independent quantum conference key agreement

TL;DR

This paper establishes fundamental upper bounds on the rate of device-independent conference key agreement in quantum networks, highlighting inherent limitations and the gap with device-dependent protocols.

Contribution

It introduces new upper bounds based on multipartite entanglement measures and compares them with existing protocols, revealing intrinsic limitations in DI-CKA.

Findings

Derived upper bounds using multipartite squashed entanglement

Compared bounds with known protocol rates

Identified gaps between device-independent and device-dependent key rates

Abstract

We provide several general upper bounds on the rate of a key secure against a quantum adversary in the device-independent conference key agreement (DI-CKA) scenario. They include bounds by reduced entanglement measures and those based on multipartite secrecy monotones such as a multipartite squashed entanglement-based measure, which we refer to as reduced c-squashed entanglement. We compare the latter bound with the known lower bound for the protocol of conference key distillation based on the parity Clauser-Horne-Shimony-Holt game. We also show that the gap between the DI-CKA rate and the device-dependent rate is inherited from the bipartite gap between device-independent and device-dependent key rates, giving examples that exhibit the strict gap.