Device-independent tests of quantum measurements

TL;DR

This paper provides a complete characterization of input-output correlations generated by any qubit measurement, offering optimal device-independent tests and insights into the geometry of quantum measurement sets.

Contribution

It introduces a closed-form, full characterization of correlations for qubit measurements, including special cases like SIC measurements and mutually unbiased bases, with noise considerations.

Findings

Complete correlation set characterization for qubit measurements

Optimal device-independent tests of quantum measurements

Geometrical interpretation of measurement correlation sets

Abstract

We consider the problem of characterizing the set of input-output correlations that can be generated by an arbitrarily given quantum measurement. Our main result is to provide a closed-form, full characterization of such a set for any qubit measurement, and to discuss its geometrical interpretation. As applications, we further specify our results to the cases of real and complex symmetric, informationally complete measurements and mutually unbiased bases of a qubit, in the presence of isotropic noise. Our results provide the optimal device-independent tests of quantum measurements.