New Protocols for Conference Key and Multipartite Entanglement Distillation
Farzin Salek, Andreas Winter
TL;DR
This work addresses multipartite conference key agreement and GHZ distillation in the source-model of quantum networks with quantum side information. It introduces a quantum analogue of communication for omniscience and develops non-interactive protocols that yield lower bounds on the distillable conference key $K_{n.i.}( ho)$ and the GHZ distillation capacity $D_{n.i.}( ho)$, including a coherent variant that enables direct GHZ generation. Two constructive GHZ-distillation routes from mixed states are proposed: (i) entanglement combing to generate EPR links and teleport to GHZ with a star-structure bound, and (ii) spanning-tree assisted distillation using $E_A(i:j|\rho)$ to optimize GHZ yield; a coherent secret-key protocol is also developed to facilitate GHZ generation from a purification, though coherence can constrain the GHZ rate relative to the key rate. The results illustrate that omniscience-based approaches are not universally optimal among non-interactive protocols and provide a framework for analyzing the tradeoffs between secret-key and GHZ entanglement generation in networks with eavesdroppers. Overall, the paper provides explicit achievable rates and constructive protocols that advance secure multiparty key distribution and multipartite entanglement distillation in quantum networks with quantum side information.
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.