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.

翻译：我们研究了量子信息处理在网络中的两个相互关联的问题：会议密钥协商和纠缠蒸馏，两者均基于所谓的源模型，其中给定资源是一个多方量子态，参与者通过公共经典信道交互以生成所需关联。第一个问题是当源态在合法参与者与窃听者之间共享时，如何蒸馏会议密钥；窃听者除了初始拥有此量子侧信息外，还能观测参与者之间的公共通信。第二个问题是通过局域操作和经典通信从给定混合态蒸馏出格林伯格-霍恩-蔡林格态。这些问题的设置扩展了我们之前的论文[IEEE Trans. Inf. Theory 68(2):976-988, 2022]，并推广了其结果：利用全知通信任务的量子版本，我们推导了通过非交互通信协议从任意多方量子态蒸馏可蒸馏会议密钥的新下界。其次，我们从多方混合态建立了GHZ态产率的新下界。具体而言，我们提出了两种方法在足够多的节点间产生二分纠缠，从而制备GHZ态。接着，我们证明在某些条件下会议密钥协商协议可被相干化，从而直接生成多方GHZ态。