Self-Testing of Symmetric Three-Qubit States
Xinhui Li, Yukun Wang, Yun-Guang Han, Su‐Juan Qin, Fei Gao, Qiaoyan Wen · IEEE Journal on Selected Areas in Communications · 2020
Self-testing refers to a device-independent way to uniquely identify an unknown quantum device based only on the observed statistics. Earlier results on self-testing of multipartite state were restricted either to Dicke states or Graph states. In this paper, we propose self-testing schemes for a large family of symmetric three-qubit states, namely the superposition of W state and GHZ state. We first propose and analytically prove a self-testing criterion for the special symmetric state with equal coefficients of the canonical bases, by designing subsystem self-testing of partially and maximally entangled state simultaneously. Then we demonstrate for the general case, the states can be self-tested numerically by the swap method combining semidefinite programming (SDP) in high precision.