期刊
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
卷 38, 期 3, 页码 589-597出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JSAC.2020.2968994
关键词
Entanglement; symmetric states; self-testing; Bell inequality
资金
- National Nature Science Foundation of China [61671082, 61672110, 61972048, 61976024, 61572081, 11875110]
- Fundamental Research Funds for the Central Universities [2019XD-A01]
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.
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