Certification of incompatible measurements using quantum steering

In recent years nonlocality has been extensively explored as a resource for self-testing -- a device-independent way of certification of entangled quantum states and measurements performed on them. However, most of the efforts in designing self-testing schemes were concerned with entangled quantum states, leaving the problem of certification of quantum measurements largely unexplored. Here we address this problem, concentrating on a simpler, one-sided device-independent scenario. We propose a simple scheme for certification of any set of d-outcome projective measurements which do not share any common invariant subspace, termed here genuinely incompatible, and the maximally entangled state of two qudits. We also study robustness of our self-testing statements for a certain class of genuinely incompatible measurements including mutually unbiased bases.Comment: Stronger self-testing with less assumptions than version