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Self-testing is a method to certify quantum states and measurements in adevice-independent way. The device-independent certification of quantumproperties is purely based on input-output measurement statistics of theinvolved devices with minimal knowledge about their internal workings.Bipartite pure entangled states can be self-tested, but, in the case ofmultipartite pure entangled states, the answer is not so straightforward.Nevertheless, \v{S}upi\'{c} et al. recently introduced a novel self-testingmethod for any pure entangled quantum state, which leverages network assistanceand relies on bipartite entangled measurements. Hence, their scheme loses thetrue device-independent flavor of self-testing. In this regard, we provide aself-testing scheme for genuine multipartite pure entangle states in the truesense by employing a generalized Hardy-type non-local argument. Our schemeinvolves only local operations and classical communications and does not dependon bipartite entangled measurements and is free from any network assistance. Inaddition, we provide the device-independent bound of the maximum probability ofsuccess for generalized Hardy-type nonlocality argument.

Network-assist free self-testing of genuine multipartite entangled states