Asymmetric quantum network based on multipartite Einstein–Podolsky–Rosen steering

In this work, we propose an asymmetric multi-user access optical network with hierarchical structure in terms of steering ability. The N-partite system is generated by mixing two squeezed lights and N−2 vacuum modes at N−1 beam splitters. The asymmetry of this system can be constructed by choosing proper reflectivities of beam splitters and introducing asymmetric loss to channels of the network, such that the steering ability is distributed asymmetrically among users. By proper construction, one superior in the network possesses higher steering ability than any one of the remaining N−1 subordinates. We show how to accomplish the directional quantum steering between them, i.e., the superior can apparently steer any subordinate’s state, but it cannot always happen in the opposite direction. In addition, we quantify the thresholds of loss tolerance that will prevent the extraction of information of the superior by M(1≤M≤N−1) subordinates’ local measurements. An important feature of such a network is that the superior can send a secret message to certain subordinates without trustworthy assumptions about them and their apparatus. Our findings have applications in one-sided device-independent quantum communication protocol with multi-users.