Certification of incompatible measurements using quantum steering

TL;DR

This paper introduces a method to certify genuinely incompatible quantum measurements using quantum steering in a one-sided device-independent scenario, with applications to quantum cryptography.

Contribution

It presents a simple scheme for certifying genuinely incompatible measurements and analyzes robustness for key measurement classes like mutually unbiased bases.

Findings

Certifies any set of $d$-outcome projective measurements without common invariant subspaces.

Utilizes quantum steering in a one-sided device-independent framework.

Demonstrates robustness for mutually unbiased bases in quantum cryptography.

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.