Certification of incompatible measurements using quantum steering

In this Letter we consider the problem of the 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 a one-sided device-independent scenario where the resource employed for certification is quantum steering. We also study the 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.

Automated summary

In this letter, we discuss the certification problem of quantum measurements and propose a simple scheme for certifying incompatible projective measurements and the maximally entangled state. We also study the robustness of self-testing results for genuinely incompatible measurements.