Self-testing of genuine multipartite non-local and non-maximally entangled states

Self-testing is pivotal in characterizing quantum systems with minimal internal assumptions, representing the most robust certification method. In the existing self-testing literature, self-testing states that are not maximally entangled, but exhibit genuine multipartite nonlocality, have remained an open problem, a crucial issue given its significance in understanding many-body systems. Addressing this gap, we introduce a Cabello-like paradox applicable to scenarios involving any number of parties, offering a means to detect genuine multipartite nonlocality. This paradox facilitates the identification and self-testing of states that push its limits, notably non-maximally multipartite entangled states. While recent results (Šupić et al., 2023 [32]) suggest network self-testing as a means to self-test all quantum states, here we operate within the standard self-testing framework to self-test genuine multipartite non-local and non-maximally entangled states.