A timely enterprise nowadays is understanding which states can bedevice-independently self-tested and how. This question has been answeredrecently in the bipartite case [Nat. Comm. 8, 15485 (2017)], while it islargely unexplored in the multipartite case, with only a few scattered results,using a variety of different methods: maximal violation of a Bell inequality,numerical SWAP method, stabilizer self-testing etc. In this work, weinvestigate a simple, and potentially unifying, approach: combining projectionsonto two-qubit spaces (projecting parties or degrees of freedom) and then usingmaximal violation of the tilted CHSH inequalities. This allows to obtainself-testing of Dicke states and partially entangled GHZ states with twomeasurements per party, and also to recover self-testing of graph states(previously known only through stabilizer methods). Finally, we give the firstself-test of a class multipartite qudit states: we generalize the self-testingof partially entangled GHZ states by adapting techniques from [Nat. Comm. 8,15485 (2017)], and show that all multipartite states which admit a Schmidtdecomposition can be self-tested with few measurements.
展开▼
