Fig. 2: A schematic representation of the self-testing scenario for five-partite states.
From: All pure multipartite entangled states of qubits can be self-tested
Every party in a given sub-test plays one of two roles: a projecting party (blue) is a party whose local dichotomic measurement denoted with lozenge is used to collapse the global state and thereby prepare different two-party reduced states for certification; a tested party (purple) is one of the two parties whose post-measurement two-party state is being certified in that sub-test. In each sub-test for a five-partite state, three projecting parties receive the lozenge-input,and the resulting projected states of the two tested parties are then self-tested. The correlations corresponding to the output 1 of a projecting party contribute to the self-testing of the tested parties' states only in sub-tests that occur before the projecting party itself assumes the role of a tested party. In this case, the first sub-test self-tests 23 distinct states, corresponding to 23 different global outputs from the projecting parties. In the second sub-test, this number reduces to 22, then to 2 in the third sub-test, and finally, the last sub-test self-tests a single state corresponding to one specific global output.
