New Protocols for Conference Key and Multipartite Entanglement Distillation

TL;DR

This paper introduces new protocols for conference key agreement and multipartite entanglement distillation in quantum networks, providing lower bounds and methods for generating GHZ states from multipartite quantum states.

Contribution

It extends previous work by deriving novel lower bounds on distillable conference key and GHZ state yield using quantum communication protocols and coherence techniques.

Findings

Derived lower bounds on distillable conference key from multipartite states.

Established methods to produce GHZ states from mixed states.

Demonstrated coherence in conference key protocols enabling direct GHZ state generation.

Abstract

We approach two interconnected problems of quantum information processing in networks: Conference key agreement and entanglement distillation, both in the so-called source model where the given resource is a multipartite quantum state and the players interact over public classical channels to generate the desired correlation. The first problem is the distillation of a conference key when the source state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of local operations and classical communication (LOCC) from the given mixed state. These problem settings extend our previous paper [IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive novel lower bounds on the distillable conference key from any multipartite quantum state by means of non-interacting communication protocols. Secondly, we establish novel lower bounds on the yield of GHZ states from multipartite mixed states. Namely, we present two methods to produce bipartite entanglement between sufficiently many nodes so as to produce GHZ states. Next, we show that the conference key agreement protocol can be made coherent under certain conditions, enabling the direct generation of multipartite GHZ states.