Certifying sets of quantum observables with any full-rank state

TL;DR

This paper demonstrates that certain sets of quantum observables can be uniquely certified using any full-rank initial state, enabling robust experimental verification of quantum systems and linking two major certification methods.

Contribution

It introduces the concept of certification with any full-rank state (CFR) for finite-dimensional quantum systems, establishing its feasibility, robustness, and connection to Bell self-testing.

Findings

CFR is possible for all finite dimensions d ≥ 3

Complete Kochen-Specker sets can be Bell self-tested if they enable CFR

CFR is robust and experimentally useful in dimensions 3 and 4

Abstract

We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this ``certification with any full-rank state'' (CFR) is possible for any quantum system of finite dimension $d \ge 3$ and is robust and experimentally useful in dimensions 3 and 4. In addition, we prove that complete Kochen-Specker sets can be Bell self-tested if and only if they enable CFR. This establishes a fundamental connection between these two methods of certification, shows that both methods can be combined in the same experiment, and opens new possibilities for certifying quantum devices.