Certifying classes of $d$-outcome measurements with quantum steering

TL;DR

This paper introduces a family of steering inequalities for certifying large classes of d-outcome quantum measurements and maximally entangled states, broadening semi-DI certification methods.

Contribution

It constructs new steering inequalities tailored for d-outcome measurements and proves their effectiveness for self-testing without assuming pure states or projective measurements.

Findings

Maximal quantum violation certifies the measurements and entangled states.

The inequalities are robust to noise.

The approach broadens semi-DI certification scope.

Abstract

Device-independent (DI) certification schemes are based on minimal assumptions about the quantum system under study, which makes the most desirable among certification schemes. However, they are often the most challenging to implement. In order to reduce the implementation cost one can consider semi-DI (SDI) schemes such as those based on quantum steering. Here we provide a construction of a family of steering inequalities which are tailored to large classes of d-outcomes projective measurements being a certain linear combination of the Heisenberg-Weyl operators on the untrusted side and a fixed set of known measurements on the trusted side. We then prove that the maximal quantum violation of those inequalities can be used for certification of those measurements and the maximally entangled state of two qudits. Importantly, in our self-testing proof, we do not assume the shared state to be pure, nor do we assume the measurements to be projective. Before concluding, we also show how robust to noise our self-testing statement is. We believe that our construction broadens the scope of SDI certification, paving the way for more general but still less costly quantum certification protocols.