We consider the distribution of secret keys, both in a bipartite and a multipartite (conference) setting, via a quantum network and establish a framework to obtain bounds on the achievable rates. We show that any multipartite private state--the output of a protocol distilling secret key among the trusted parties--has to be genuinely multipartite entangled. In order to describe general network settings, we introduce a multiplex quantum channel, which links an arbitrary number of parties, where each party can take the role of sender only, receiver only, or both sender and receiver. We define asymptotic and non-asymptotic LOCC-assisted secret-key-agreement (SKA) capacities for multiplex quantum channels and provide strong and weak converse bounds. The structure of the protocols we consider, manifested by an adaptive strategy of secret key and entanglement [Greenberger-Horne-Zeilinger (GHZ state)] distillation over an arbitrary multiplex quantum channel, is generic. As a result, our approach also allows us to study the performance of quantum key repeaters and measurement-device-independent quantum key distribution (MDI-QKD) setups. For teleportation-covariant multiplex quantum channels, we get upper bounds on the SKA capacities in terms of the entanglement measures of their Choi states. We also obtain bounds on the rates at which secret key and GHZ states can be distilled from a finite number of copies of an arbitrary multipartite quantum state. We are able to determine the capacities for MDI-QKD setups and rates of GHZ-state distillation for some cases of interest.
翻译:我们考虑通过量子网络在双方和多方(会议)设置中分配秘密钥匙,通过量子网络和多方(会议)设置来分配秘密钥匙,并通过量子网络建立一个框架,以获得可实现利率的界限。我们表明,任何多方私营国家输出,在受信任的各方之间蒸馏秘密钥匙,必须是真正多方纠缠的。为了描述一般网络设置,我们引入了一个多式量子频道,将任意数目的各方联系起来,其中各方只能发挥发送方、接收方或数量发送方和接收方的作用。因此,我们的方法还使我们能够在多式量式LOC(LOC)辅助的量子协议(SKKA)能力方面,确定多式量子频道(S-KKA)的无线性能,提供强大和薄弱的反向界限。我们所考虑的协议结构,表现为秘密键盘[Granberger-Horne-Zelinger (GHHZ) 的调和任意性多式多式多式量子频道。我们的方法还让我们在S-D-D-S-devely-deal-D-Slaction Slaction Slaction Slaction Slaction Slaction Slaction 能力中进行量-s-destration 的量子输出的量子输出能力。