Certification of incompatible measurements using quantum steering

Abstract

In this letter we consider the problem of certification of quantum measurements with an arbitrary number of outcomes. We propose a simple scheme for certifying any set of $d$-outcome projective measurements which do not share any common invariant proper subspace, termed here genuinely incompatible, and the maximally entangled state of two qudits. For our purpose, we focus on a simpler scenario, termed as one-sided device-independent scenario where the resource employed for certification is quantum steering. We also study robustness of our self-testing statements for a certain class of genuinely incompatible measurements including mutually unbiased bases which are essential for several quantum information-theoretic tasks such as quantum cryptography.